- Allow your students to effortlessly switch among visual, numerical, and algebraic representations of calculus concepts.
- Shift emphasis from manipulative skills to fundamental calculus ideas.
- Improve students’ engagement (as well as concept understanding and retention) by exploring more realistic problems earlier.
- Communicate mathematical ideas using a single script that includes explanatory text, formulas, pictures, as well as MATLAB commands, outputs and graphics.
- Use powerful symbolic and numerical routines that don’t stand in the way of mathematical thinking.
- Allow your students to easily check results, formulate, test and revise their own hypothesis.
- Allow students to discover calculus truths on their own using inductive as well as deductive reasoning.
- Introduce your students to world-class mathematical software that will help them throughout their studies and careers, thereby increasing their success with calculus and math.
Some Benefits of Using Computation in Calculus Courses:
Research shows that the thoughtful inclusion of computation in calculus courses (Murphy, 2006) provides a dynamic, hands-on, learning environment (Vasquez, 2015), promotes concept understanding (Awang, Zakaria, 2013, Leng et. al. 2009), keeps students engaged (Colonna, Easley, 2011), and increases their competence and confidence (Merriweather, Tharp, 1999).
Calculus 1 at Texas A&M University (symbolic):
Calculus 2 at Texas A&M University (symbolic):
Calculus 1 at University of Maryland (symbolic):
Other Calculus course materials (numerical):
Pre-Calculus and Algebra:
- Solving Algebraic Equations Symbolically (11:54)
- Solving Systems of Algebraic Equations Symbolically (12:11)
- Defining Functions in MATLAB (7:16)
- Limits using MATLAB (6:31)
- Derivatives using MATLAB (6:26)
- Evaluating Derivatives at a point (5:37)
- Partial Derivatives using MATLAB (8:37)
- Indefinite and Definite Integrals (9:10)
- Calculus Operations with MATLAB (22:34)
Differential Equations and Linear Algebra:
- Learn Differential Equations
- Differential Equations and Linear Algebra Course by Gilbert Strang (MIT)
- Solve ODEs in MATLAB (MIT Courseware)
- Solving Ordinary Differential Equations with MATLAB (self paced course)
Curriculum Usage Examples:
- Mathematics Undergraduate Students at the University of Oxford Use MATLAB for Symbolic Computation and Problem Solving
- Manchester Metropolitan University Students Vote Math Best Overall Course Following Adoption of MATLAB
- Chalmers University of Technology Integrates MATLAB Throughout Core Mathematics Curriculum
- Using MATLAB to Teach Problem-Solving Techniques to First-Year Liberal Arts Students
Documentation, Examples, and Textbooks:
An introduction to Symbolic Math Toolbox utilities for calculus:
Common calculus topics in the Symbolic Math Toolbox documentation:
- Taylor Series
- Solve Differential Equations
- Ordinary Differential Equations
Other Symbolic Math Toolbox examples:
- Analytical Plotting with Symbolic Math Toolbox
- Find Asymptotes, Critical and Inflection Points
- List of all examples
Numerical functions commonly used in calculus:
Some calculus textbooks using MATLAB:
More MATLAB Information:
Learn MATLAB in 2 hours:
- MATLAB Onramp, a free, interactive tutorial (and other self-paced courses)
Free Auto Grading:
MATLAB in Industry: