Biomedical engineering is the broad area of study in which engineers use an interdisciplinary approach to solve problems in the medical field, oftentimes associated with the interaction between living and non-living systems. The breadth of solution methodologies requires biomedical engineers to take a quantitative approach to system analysis in "traditional" engineering fields, while simultaneously employing a fundamental understanding of the relevant life sciences. Biomedical engineers should be prepared to design, build, test, and/or analyze biological systems, diagnostics, devices, and treatment modalities. Examples of current areas of research and education include:

• Biomechanics (Scaling from systems to tissues, cells, and molecules)
• Biomedical imaging
• Biomaterials and Tissue engineering
• Cardiovascular engineering
• Biophotonics
• Neural engineering
• Orthopedic engineering
• Biomedical instrumentation and devices

A variety of logical, interdisciplinary course sequences allow thematic approaches to the above areas (eg. biology-based, physics-based, computer-based, mechanics/materials-based, etc.).

Recommended Courses

• ENGS 34: Fluid Mechanics
• ENGS 35: Biotechnology and Biochemical Engineering
• ENGS 36: Chemical Engineering
• PHYS 19: Introductory Physics III
• MATH 22: Linear Algebra with Applications
• MATH 23: Differential Equations
• CHEM 41: Biological Chemistry I
• CHEM 51 & 52: Organic Chemistry or CHEM 57 & 58: Honors Organic Chemistry
• BIOL 40: Biochemistry
• ENGS 56: Introduction to Biomedical Engineering
• ENGS 57: Intermediate Biomedical Engineering or ENGS 169: Intermediate Biomedical Engineering
• ENGS 59: Basic Biological Circuit Engineering
• ENGS 111: Digital Image Processing
• ENGS 129: Biomedical Circuits and Systems
• ENGS 160: Biotechnology and Biochemical Engineering
• ENGS 165: Biomaterials
• ENGS 166: Quantitative Human Physiology
• ENGS 167: Medical Imaging
• ENGG 168: Biomedical Radiation Transport
• ENGS 170: Neuroengineering
• As appropriate: Electrical Engineering, Control, Mechanical Engineering, Bioengineering, Design, Computer Engineering, and Neuropsychology courses to provide tools for solving problems in the above-mentioned courses.
• Individuals wishing to explore biological approaches are encouraged to reference the description for ENGS 35: Biotechnology and Biochemical Engineering and enroll in it to gain exposure to this space.

Biological engineering exists at the interface of engineering, biological, and chemical sciences. This interdisciplinary field brings to bear fundamental design principles to both elucidate and modulate the function of biological systems, ranging in scale from molecular to cellular to whole organisms. The bioengineer’s toolbox may include skills such as modeling, big data analysis, genetics, process design, biochemistry, and molecular, micro, and cellular biology. By designing, engineering, and optimizing biological systems, bioengineers and biotechnologists are seeking to tackle key unmet needs in medicine, agriculture, industry, the environment, consumer markets, etc.

Recommended Courses

These assume that ENGS 35: Biotechnology and Biochemical Engineering is taken as a Gateway course.

• ENGS 34: Fluid Mechanics
• ENGS 58: Introduction to Protein Engineering
• ENGS 59: Basic Biological Circuit Engineering
• ENGS 157: Chemical Process Design
• ENGS 158: Chemical Kinetics and Reactors
• ENGS 161: Metabolic Engineering
• ENGS 162: Basic Biological Circuit Engineering
• ENGS 165: Biomaterials
• COSC 75: Introduction to Bioinformatics
• COSC 86: Computational Structural Biology
• COSC 89: Topics in Applied Computer Science (any topically relevant course in this series of courses)
• CHEM 40: Physical Chemistry of Biochemical Processes
• CHEM 41: Biological Chemistry I
• CHEM 51 & 52: Organic Chemistry or CHEM 57 & 58: Honors Organic Chemistry
• BIOL 40: Biochemistry
• BIOL 45: Molecular Biology
• BIOL 46: Microbiology
• BIOL 47: Genomics: From Data to Analysis

Chemical engineering is a foundational field that is centered on designing and optimizing processes that involve the physical and chemical transformation of matter. The chemical engineer’s toolbox may include skills such as process design, heat and mass transfer, chemical transformations and kinetics, molecular and cellular biology, and others. By designing and optimizing processes, chemical engineers tackle broad problems in biological, chemical, energy, and environmental systems.

Recommended Courses

These assume that ENGS 36: Chemical Engineering is taken as a Gateway course.

• ENGS 34: Fluid Mechanics
• ENGS 132: Thermodynamics and Kinetics in Condensed Phases
• ENGS 150: Intermediate Fluid Mechanics
• ENGS 155: Intermediate Thermodynamics
• ENGS 156: Heat, Mass, and Momentum Transfer
• ENGS 157: Chemical Process Design
• ENGS 158: Chemical Kinetics and Reactors
• CHEM 51 & 52: Organic Chemistry or CHEM 57 & 58: Honors Organic Chemistry
• CHEM 75: Physical Chemistry I
• CHEM 93: Physical Organic Chemistry
• CHEM 96.02: Statistical Thermodynamics
• CHEM 96.07: Introduction to Materials Chemistry

Computer engineering is a rapidly expanding field that is focused on designing, building, and analyzing computational and networked information processing systems. A computer engineer understands the hardware, software, and applications environment of computing systems. As a result, computer engineers must be familiar with computer architectures, networks, and applications software as well as modeling and analysis techniques for such systems including machine learning, complex systems, and artificial intelligence. Computer engineers are involved in modern systems ranging from mobile social networking applications to highly autonomous vehicles to smart sensor networks to biomedical and smart energy devices.

Recommended Courses

These assume that ENGS 31: Digital Electronics is taken as a Gateway course.

• ENGS 32: Electronics: Introduction to Linear and Digital Circuits
• ENGS 62: Microprocessors in Engineered Systems
• ENGS 65: Engineering Software Design
• ENGS 67: Programming Parallel Systems
• ENGS 68: Introduction to Communication Systems
• ENGS 69: Smartphone Programming
• ENGS 108: Applied Machine Learning
• ENGS 112: Modern Information Technologies
• ENGS 115: Parallel Computing
• ENGS 128: Advanced Digital System Design
• ENGS 147: Mechatronics
• COSC 50: Software Design and Implementation
• COSC 51: Computer Architecture
• COSC 58: Operating Systems
• COSC 60: Computer Networks
• COSC 70: Foundations of Applied Computer Science
• COSC 71: Numerical Methods in Computation
• COSC 72: Accelerated Computer Linguistics
• COSC 73: Computational Aspects of Digital Photography
• COSC 74: Machine Learning and Statistical Data Analysis
• COSC 75: Introduction to Bioinformatics
• COSC 76: Artificial Intelligence
• COSC 77: Computer Graphics
• COSC 78: Deep Learning
• COSC 81: Principles of Robot Design and Programming
• COSC 83: Computer Vision
• COSC 84: Mathematical Optimization and Modeling
• COSC 86: Computational Structural Biology
• COSC 87: Rendering Algorithms
• COSC 89: Topics in Applied Computer Science (any topically relevant course in this series of courses)

Recommended Courses for Computer Science Major + Engineering Sciences Minor

This sample program shows the courses for the computer science major plus engineering sciences minor and the BE program with a computer engineering concentration.

Computer Science Major

• COSC 1: Introduction to Programming and Computation
• COSC 10: Problem Solving via Object-Oriented Programming
• COSC 30: Discrete Mathematics in Computer Science
• COSC 31: Algorithms
• COSC 50: Software Design and Implementation
• COSC 51: Computer Architecture
• COSC 56: Digital Electronics (same as ENGS 31)—COSC 56 fulfills particular requirements for the BE
• COSC 71: Numerical Methods in Computation (same as ENGS 91)—COSC 71 fulfills particular requirements for the BE
• COSC 70: Foundations of Applied Computer Science or COSC 89: Topics in Applied Computer Science (any topically relevant course in this series of courses)
• Two electives chosen from COSC 30-89, not used to satisfy another requirement
• COSC 98: Senior Design and Implementation Project, or a Senior Thesis

Engineering Sciences Minor and Pre-BE Courses

• MATH 3: Calculus
• MATH 8: Calculus of Functions of One and Several Variables
• MATH 11: Accelerated Multivariable Calculus or MATH 13 Calculus of Vector-Valued Functions
• CHEM 5: General Chemistry
• PHYS 13: Introductory Physics I
• PHYS 14: Introductory Physics II
• ENGS 21: Introduction to Engineering
• ENGS 22: Systems
• ENGS 23: Distributed Systems and Fields
• ENGS 32: Electronics: Introduction to Linear and Digital Circuits

BE (Fifth Year) Courses

• ENGS 26: Control Theory
• ENGS 27: Discrete and Probabilistic Systems
• ENGS 62: Microprocessors in Engineered Systems
• ENGS 67: Programming Parallel Systems or ENGS 115: Parallel Computing
• ENGS 89: Engineering Design Methodology and Project Initiation
• ENGS 90: Engineering Design Methodology and Project Completion
• ENGS 112: Modern Information Technologies, or ENGS 128: Advanced Digital System Design, or ENGS 147: Mechatronics

Recommended Courses for Computer Science Major Modified with Engineering

This sample program shows the courses for the computer science major modified with engineering and the BE program with a computer engineering concentration.

Modified Major

• COSC 1: Introduction to Programming and Computation or ENGS 20: Introduction to Scientific Computing
• COSC 10: Problem Solving via Object-Oriented Programming
• MATH 3: Introduction to Calculus
• MATH 8: Calculus of Functions of One and Several Variables
• MATH 11: Multivariable Calculus for Two-Term Advanced Placement First-Year Students or MATH 13 Calculus of Vector-Valued Functions
• PHYS 13: Introductory Physics I
• PHYS 14: Introductory Physics II
• COSC 30: Discrete Mathematics in Computer Science
• COSC 31: Algorithms
• COSC 50: Software Design and Implementation
• COSC 51: Computer Architecture
• COSC 71: Numerical Methods in Computation (same as ENGS 91)—COSC 71 fulfills a particular requirement for the BE
• One elective chosen from COSC 30-89, not used to satisfy another requirement
• ENGS 22: Systems
• ENGS 31: Digital Electronics
• ENGS 32: Electronics: Introduction to Linear and Digital Circuits
• ENGS 62: Microprocessors in Engineered Systems
• COSC 98: Senior Design and Implementation Project, or a Senior Thesis

Pre-BE Courses

• CHEM 5: General Chemistry
• ENGS 21: Introduction to Engineering

BE (Fifth Year) Courses

• ENGS 23: Distributed Systems and Fields
• ENGS 26: Control Theory
• ENGS 27: Discrete and Probabilistic Systems
• ENGS 67: Programming Parallel Systems or ENGS 115: Parallel Computing
• ENGS 89: Engineering Design Methodology and Project Initiation
• ENGS 90: Engineering Design Methodology and Project Completion
• ENGS 112: Modern Information Technologies, or ENGS 128: Advanced Digital System Design, or ENGS 147: Mechatronics

Electrical engineering harnesses the phenomena of electricity to develop technologies ranging from semiconductor devices to advanced communication networks. There are numerous subfields within this very broad discipline, all built on the foundations of mathematics and computer science, physical and life sciences, electromagnetics, electronics, and systems. The sample BE program reflects this breadth and begins to cultivate depth in certain areas. Graduate study at the MS and PhD level enables further specialization. Students are urged to meet with a faculty advisor to work out a plan of study within the guidelines of the sample program.

Recommended Courses

Mathematics and Basic Science Applied Math

• ENGS 92: Fourier Transforms and Complex Variables

Mathematics and Basic Science Electives

• MATH 22: Linear Algebra with Applications
• MATH 23: Differential Equations
• PHYS 19: Introductory Physics III

Engineering Gateway

• ENGS 31: Digital Electronics
• ENGS 32: Electronics: Introduction to Linear and Digital Circuits

Engineering Electives

• ENGS 59: Basic Biological Circuit Engineering
• ENGS 60: Introduction to Solid-State Electronic Devices
• ENGS 61: Intermediate Electrical Circuits
• ENGS 62: Microprocessors in Engineered Systems
• ENGS 64: Engineering Electromagnetics
• ENGS 68: Introduction to Communication Systems
• ENGS 110: Signal Processing
• ENGS 111: Digital Image Processing
• ENGS 120: Electronic Waves: Analytical and Modeling Approaches
• ENGG 122: Advanced Topics in Semiconductor Devices
• ENGS 123: Optics
• ENGS 124: Optical Devices and Systems
• ENGS 125: Power Electronics and Electromechanical Energy Conservation
• ENGS 126: Analog Integrated Circuit Design
• ENGS 128: Advanced Digital System Design
• ENGS 129: Biomedical Circuits and Systems
• ENGS 145: Modern Control Theory
• ENGS 147: Mechatronics
• ENGS 149: Introduction to Systems Identification

Energy is a major determinant of world events and quality of life. Energy engineering brings to bear the spectrum of engineering disciplines on challenges and opportunities involving energy, recognizing social, political, and economic contexts. This area of study aims to increase the efficiency of energy conversion, storage, transmission, and utilization, to accelerate the transition to sustainable energy sources, and to improve access to and management of energy systems. Students are encouraged to develop depth in one or more technical areas along with a broad understanding of energy technologies, systems, challenges, and opportunities.

Recommended Courses

Engineering Distributive Core

• ENGS 25: Introduction to Thermodynamics

Engineering Electives

• ENGS 173: Energy Utilization
• ENGS 174: Energy Conversion

Environmental engineering is the application of fundamental knowledge in mathematics, natural sciences (physics, chemistry, biology), and various disciplines of engineering (mostly civil, mechanical, and chemical engineering) to solve problems and address challenges at the intersection of technology with nature. The overarching objective is to protect the environment and ensure sustainability. Problems and challenges are typicaly of two types, (1) post-technology remediation or treatment, and (2) prevention or reduction of impacts by environmentally conscious design. A systems approach prevails in both types. The environmental engineer is quintessentially an interdisciplinary engineer.

Recommended Courses

Mathematics and Basic Science Applied Math

• ENGS 93: Statistical Methods in Engineering

Mathematics and Basic Science Electives

• EARS 71: River Processes and Watershed Science
• ENVS 30: Global Environmental Science

Engineering Distributive Core

• ENGS 25: Introduction to Thermodynamics
• ENGS 27: Discrete and Probabilistic Systems
• ENGS 28: Embedded Systems

Engineering Gateway

• ENGS 36: Chemical Engineering
• ENGS 37: Introduction to Environmental Engineering

Engineering Electives

• ENGS 41: Sustainability and Natural Resource Management
• ENGS 43: Environmental Transport and Fate
• ENGS 44: Sustainable Design
• ENGS 46: Advanced Hydrology
• ENGS 151: Environmental Fluid Mechanics
• ENGS 171: Industrial Ecology
• ENGS 172: Climate Change and Engineering
• ENGS 173: Energy Utilization
• ENGS 174: Energy Conversion
• ENGS 175: Energy Systems

The study of materials science and engineering relates the properties of materials—chemical, electrical, magnetic, mechanical, optical—to their internal architecture or microstructure. In turn, the structure is related to processing—solidification, thermal/mechanical treatment, vapor deposition, etc.—and to the underlying thermodynamic "driving forces" and kinetics that underlie changes in structure and hence in properties and behavior. Fundamental to the study are both qualitative and quantitative methods of microstructural analysis.

Recommended Courses

Mathematics and Basic Science (at least 9 courses)

• MATH 3: Calculus
• MATH 8: Calculus of Functions of One and Several Variables
• MATH 13: Calculus of Vector-Valued Functions
• PHYS 13: Introductory Physics I
• PHYS 14: Introductory Physics II
• CHEM 5: General Chemistry
• MATH 23: Differential Equations
• PHYS 19: Relativistic and Quantum Physics
• PHYS 43: Statistical Physics, or other relevant mathematics and science courses
• ENGS 93: Statistical Methods in Engineering

Engineering Science (at least 14 courses)

Computer Science (1 or 2 courses)

• Option 1 (1 course): ENGS 20: Introduction to Scientific Computing (May not be taken under the non-recording option.)
• Option 2 (2 courses): COSC 1: Introduction to Programming and Computation and COSC 10: Problem Solving via Object-Oriented Programming

Core (5 courses)

• ENGS 21: Introduction to Engineering
• ENGS 22: Systems
• ENGS 23: Distributed Systems and Fields
• ENGS 24: Science of Materials
• ENGS 25: Introduction to Thermodynamics

Gateway (2 courses)

• ENGS 33: Solid Mechanics
• ENGS 32: Electronics: Introduction to Linear and Digital Circuits, or ENGS 36: Chemical Engineering

Engineering Electives (4 courses)
Undergraduate Mezzanine Course (1 course)

• ENGS 85.09: Introduction to Computational Materials Science and Engineering
• ENGS 86: Independent Project
• ENGS 88: Honors Thesis

Upper-Level Courses (3 courses)

• ENGS 132: Thermodynamics and Kinetics in Condensed Phases
• One course from
  • ENGS 130: Mechanical Behavior of Materials
  • ENGS 131: Science of Solid State Materials
  • ENGS 133: Methods of Materials Characterization
• One course from
  • ENGS 134: Nanotechnology
  • ENGS 135: Thin Films and Microfabrication Technology
  • ENGS 136: Electrochemical Energy Materials
  • ENGS 137: Molecular and Materials Design using Density Functional Theory
  • ENGS 138: Corrosion and Degradation of Materials
  • ENGS 165: Biomaterials

Capstone Design Project (2 courses)

• ENGS 89: Engineering Design Methodology and Project Initiation
• ENGS 90: Engineering Design Methodology and Project Completion

Mechanical engineers apply principles of engineering to the design, analysis, and manufacture of machines ranging from power systems, industrial equipment, and vehicles to athletic equipment and medical devices. Mechanical engineering is one of the broadest engineering disciplines, and as such, mechanical engineering programs should include mechanics, materials, thermal and fluid systems, and systems and controls. Programs should be planned in consultation with your faculty advisor.

Recommended Courses

Mathematics and Basic Science Electives

• MATH 22: Linear Algebra with Applications
• MATH 23: Differential Equations

Engineering Common Core

• ENGS 20: Introduction to Scientific Computing
• ENGS 21: Introduction to Engineering (Should be taken sophomore year.)
• ENGS 22: Systems
• ENGS 23: Distributed Systems and Fields

Engineering Distributive Core

• ENGS 24: Science of Materials
• ENGS 25: Introduction to Thermodynamics
• ENGS 26: Control Theory

Engineering Gateway

• ENGS 31: Digital Electronics
• ENGS 32: Electronics: Introduction to Linear and Digital Circuits
• ENGS 33: Solid Mechanics
• ENGS 34: Fluid Mechanics
• ENGS 37: Introduction to Environmental Engineering

Engineering Electives

• ENGS 71: Structural Analysis
• ENGS 72: Applied Mechanics: Dynamics
• ENGS 73: Materials Processing and Selection
• ENGS 76: Machine Engineering
• ENGS 110: Signal Processing
• ENGS 130: Mechanical Behavior of Materials
• ENGS 145: Modern Control Theory
• ENGS 146: Computer-Aided Mechanical Engineering Design
• ENGS 147: Mechatronics
• ENGG 148: Structural Mechanics
• ENGG 149: Introduction to Systems Identification
• ENGS 150: Intermediate Fluid Mechanics
• ENGS 155: Intermediate Thermodynamics
• ENGS 156: Heat, Mass, and Momentum Transfer
• ENGS 171: Industrial Ecology
• ENGS 172: Climate Change and Engineering
• ENGS 173: Energy Utilization
• ENGS 174: Energy Conversion
• ENGS 175: Energy Systems

Engineering Physics Major

This sample program shows the courses for the engineering physics major and the BE program with a mechanical engineering concentration.

Mathematics

• MATH 3: Introduction to Calculus
• MATH 8: Calculus of Functions of One and Several Variables
• MATH 11: Multivariable Calculus for Two-Term Advanced Placement First-Year Students or MATH 13: Calculus of Vector-Valued Functions
• MATH 23: Differential Equations

Chemistry

• CHEM 5: General Chemistry

Physics

• PHYS 13: Introductory Physics I
• PHYS 14: Introductory Physics II
• PHYS 19: Introductory Physics III
• PHYS 40 (formerly 24): Quantum Physics of Matter
• PHYS 43: Statistical Physics
• PHYS 44: Mechanics
• PHYS 50 (formerly 42): Introductory Quantum Mechanics

Engineering Sciences

• ENGS 20: Introduction to Scientific Computing (may not be taken under the Non-Recording Option)—ENGS 20 may be replaced by COSC 1: Introduction to Programming and Computation or COSC 10: Problem Solving via Object-Oriented Programming
• ENGS 21: Introduction to Engineering
• ENGS 22: Systems
• ENGS 23: Distributed Systems and Fields
• ENGS 24: Science of Materials
• ENGS 33: Solid Mechanics
• ENGS 76: Machine Engineering (culminating experience in the major)

BE (Fifth Year) Courses

• ENGS 25: Introduction to Thermodynamics or ENGS 26: Control Theory
• ENGS 32: Electronics: Introduction to Linear and Digital Circuits or ENGS 34: Fluid Mechanics
• ENGS 71: Structural Analysis or ENGS 72: Applied Mechanics: Dynamics
• ENGS 89: Engineering Design Methodology and Project Initiation
• ENGS 90: Engineering Design Methodology and Project Completion
• ENGS 91: Numerical Methods in Computation
• ENGS 142: Intermediate Solid Mechanics
• ENGS 146: Computer-Aided Mechanical Engineering Design

Physics Major + Engineering Sciences Minor

This sample program shows the courses for the physics major plus the engineering sciences minor and the BE program with an electrical engineering (electronics) concentration.

Mathematics

• MATH 3: Introduction to Calculus
• MATH 8: Calculus of Functions of One and Several Variables
• MATH 11: Multivariable Calculus for Two-Term Advanced Placement First-Year Students or MATH 13 Calculus of Vector-Valued Functions
• MATH 23: Differential Equations

Physics

• PHYS 13: Introductory Physics I
• PHYS 14: Introductory Physics II
• PHYS 19: Introductory Physics III
• PHYS 40 (formerly 24): Quantum Physics of Matter
• PHYS 41: Electricity and Magnetism—PHYS 41 also satisfies particular BE requirements
• PHYS 43: Statistical Physics
• PHYS 44: Mechanics or ENGS 72: Applied Mechanics: Dynamics
• PHYS 48: Electronics: Introduction to Linear and Digital Circuits (same as ENGS 32)—PHYS 48 also satisfies particular BE requirements
• PHYS 50 (formerly 42): Introductory Quantum Mechanics
• PHYS 68: Plasma Physics, or PHYS 73: Introductory Condensed Matter Physics, or PHYS 76: Methods of Experimental Physics (culminating experience in the major)

Chemistry

• CHEM 5: General Chemistry

Engineering Sciences Minor and Pre-BE Courses

• ENGS 20: Introduction to Scientific Computing (may not be taken under the Non-Recording Option)—ENGS 20 may be replaced by COSC 1: Introduction to Programming and Computation and COSC 10: Problem Solving via Object-Oriented Programming
• ENGS 21: Introduction to Engineering
• ENGS 22: Systems
• ENGS 24: Science of Materials or ENGS 27: Discrete and Probabilistic Systems
• ENGS 31: Digital Electronics
• ENGS 61: Intermediate Electrical Circuits

BE (Fifth Year) Courses

• ENGS 26: Control Theory
• ENGS 60: Introduction to Solid-State Electronic Devices or ENGS 120: Electromagnetic Fields and Waves
• ENGS 89: Engineering Design Methodology and Project Initiation
• ENGS 90: Engineering Design Methodology and Project Completion
• ENGS 92: Fourier Transforms and Complex Variables
• ENGS 110: Signal Processing
• ENGS 125: Power Electronics and Electromechanical Energy Conversion
• ENGS 126: Analog Integrated Circuit Design