Python for Engineers
UC A–G / Advanced STEM Course Proposal (Draft)
Course Length: Year-long (3 Trimesters)
Target Grade Level: 11–12
Department: Mathematics / Computer Science / Engineering
Prerequisite: Completion of AP Calculus AB (or equivalent)
Course Overview
Python for Engineers is a rigorous, year-long, project-based course designed for students who have completed at least AP Calculus AB and are interested in applying programming to solve real engineering, mathematics, and physics problems. The course introduces Python from the ground up, then progressively integrates computational mathematics, symbolic algebra, numerical methods, and physics-based modeling.
Students will learn how engineers use Python as a computational tool to analyze systems, visualize data, solve equations symbolically and numerically, and model real-world physical phenomena. Emphasis is placed on mathematical reasoning, algorithmic thinking, and engineering-style problem solving rather than general-purpose programming alone.
By the end of the course, students will be able to translate advanced math and physics concepts—including linear algebra, differential equations, and classical mechanics—into executable Python programs using industry-standard libraries such as NumPy, Matplotlib, and SymPy.
Course Goals
By the end of this course, students will:
🔹 Develop strong proficiency in Python programming for engineering applications
🔹 Use Python to visualize and analyze mathematical functions and data
🔹 Perform matrix operations and linear algebra computations programmatically
🔹 Solve algebraic, trigonometric, and calculus-based problems using symbolic computation
🔹 Apply Python to model physical systems in kinematics, dynamics, and energy
🔹 Strengthen logical thinking, debugging skills, and computational problem solving
🔹 Prepare for college-level engineering, computer science, physics, or applied mathematics coursework
Instructional Methods
🔹 Direct instruction and guided coding labs
🔹 Computational demonstrations of math and physics concepts
🔹 Engineering-style problem sets and mini-projects
🔹 Use of Jupyter Notebooks for documentation and analysis
🔹 Collaborative and individual programming assignments
🔹 Long-term applied projects each trimester
Trimester Breakdown & Units of Study
Trimester 1 – Python Foundations & Mathematical Visualization
Unit 1: Introduction to Python for Engineers
Topic Description:
Students are introduced to Python as a computational tool. The focus is on building programming fluency while connecting syntax to mathematical reasoning.
Objectives:
🔹 Write and run Python programs
🔹 Use variables, data types, conditionals, and loops
🔹 Create reusable functions
🔹 Debug programs using logical reasoning
Sample Assignment:
Students write a Python program that computes and compares multiple mathematical expressions (quadratic, trigonometric, exponential) using user-defined functions.
Unit 2: Plotting & Data Visualization with Matplotlib
Topic Description:
Students learn how engineers visualize mathematical functions and datasets.
Objectives:
🔹 Plot single-variable and multi-variable functions
🔹Customize axes, labels, legends, and grids
🔹 Visualize parametric and piecewise functions
Sample Assignment:
Students plot position, velocity, and acceleration graphs for a moving object and analyze how changes in parameters affect motion.
Unit 3: Numerical Computation with NumPy
Topic Description:
This unit introduces numerical computing and array-based operations.
Objectives:
🔹 Perform vectorized operations
🔹 Work with arrays and numerical datasets
🔹 Approximate limits, derivatives, and integrals numerically
Sample Assignment:
Students use numerical differentiation to approximate velocity and acceleration from position data and compare results with analytical solutions.
Trimester 2 – Linear Algebra, Symbolic Math & Calculus
Unit 4: Matrices & Linear Algebra for Engineering
Topic Description:
Students explore matrix operations and their applications in engineering systems.
Objectives:
🔹 Matrix addition, multiplication, and inversion
🔹 Solve systems of linear equations
🔹 Apply matrices to transformations and systems modeling
Sample Assignment:
Students model a system of equations representing currents in an electrical network and solve it using matrix methods in Python.
Unit 5: Symbolic Mathematics with SymPy
Topic Description:
Students use symbolic computation to solve math problems analytically.
Objectives:
🔹 Solve algebraic and trigonometric equations symbolically
🔹 Perform symbolic differentiation and integration
🔹 Manipulate expressions and identities
Sample Assignment:
Students use SymPy to symbolically compute derivatives and integrals of functions studied in calculus and verify results graphically.
Unit 6: Computational Calculus
Topic Description:
This unit connects calculus concepts to computation.
Objectives:
🔹 Solve optimization problems using derivatives
🔹 Analyze motion using calculus-based models
🔹 Compare symbolic and numerical solutions
Sample Assignment:
Students analyze projectile motion by solving equations symbolically and numerically, then visualizing trajectories.
Trimester 3 – Physics Modeling & Engineering Applications
Unit 7: Kinematics & Motion Modeling
Topic Description:
Students model motion in one and two dimensions using Python.
Objectives:
🔹 Simulate motion under constant and variable acceleration
🔹 Visualize trajectories and time-series data
🔹 Interpret results using physics principles
Sample Assignment:
Students build a Python simulation of a projectile launcher and analyze how angle and initial velocity affect range.
Unit 8: Forces, Energy & Dynamics
Topic Description:
Students apply Python to Newtonian mechanics and energy analysis.
Objectives:
🔹 Model forces and net acceleration
🔹 Apply work-energy principles
🔹 Simulate systems with multiple forces
Sample Assignment:
Students simulate a mass-spring system and analyze oscillatory motion using numerical integration.
Unit 9: Capstone Engineering Project (Final Exam)
Topic Description:
Students complete an individual or small-group capstone project applying Python to a real engineering problem.
Project Examples:
🔹 Physics-based simulation (motion, energy, or forces)
🔹 Computational calculus solver and visualizer
🔹 Matrix-based system model (structures, circuits, or transformations)
Deliverables:
🔹 Fully documented Python program
🔹 Mathematical and/or physics explanation
🔹 Visualizations and analysis
🔹 Formal presentation or technical report
Assessment Methods
🔹 Programming labs and assignments
🔹 Quizzes on computational math concepts
🔹 Trimester projects
🔹 Final capstone project
🔹 Code readability, correctness, and documentation
Resources / References
• Python for Data Analysis – Wes McKinney
• Numerical Methods in Engineering with Python – Jaan Kiusalaas
• MIT OpenCourseWare: Computational Science & Engineering
• NumPy, Matplotlib, and SymPy official documentation
• Jupyter Notebook environment
Conclusion
Python for Engineers bridges advanced mathematics, physics, and computation in a manner consistent with college-level engineering coursework. Students complete the course with a powerful computational toolkit and the ability to translate theoretical concepts into working simulations and analyses—preparing them for success in engineering, physics, computer science, and applied mathematics pathways.
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