Syllabus: Mastering Mathematics for Engineers: Calculus I: from functions to differential equations
Index
This course is part of our Mastering Mathematics for Engineers program: a series of MOOCs to refresh and review your bachelor level mathematics. This is the first of two Calculus MOOCs - Calculus I.
In this course we focus on functions of one variable. In the first five weeks of the course, you will learn all the basic integration, differentiation and approximation techniques required in a first calculus course of an engineering bachelor education. In the final week these topics will all come together as you solve and analyze several ordinary differential equations.
We use examples that are based on real-life applications and allow you to practice your mathematical skills in an engineering context.
Learning objectives
1. Apply differentiation techniques such as the chain rule and implicit differentiation.
2. Apply integration techniques such as integration-by-parts and substitution.
3. Solve ordinary differential equations that are important in engineering like a damped, forced harmonic oscillator.
4. Compute horizontal asymptotes to find equilibria and growth rates.
5. Analyze challenging engineering problems using these techniques.
Week 1: Functions, graphs, inverse functions, inverse trigonometric functions, compositions of functions
Week 2: Differentiation, tangent lines, implicit differentiation, differentiation of inverses
Week 3: Approximation errors, Linear approximation, Differentials, Taylor polynomials, Taylor’s inequality
Week 4: Horizontal asymptotes, Growth rates, computing horizontal asymptotes
Week 5: Integration, Integration by parts, Substitution method, integration by Taylor polynomial, integrals over unbounded domains
Week 6: Differential equations, direction fields, first order separable and linear equations, forced and damped harmonics oscillators, approximating solutions to differential equations using Taylor polynomials.
Resources and exercises (Grasple)
Before you start with the course activities and materials, it is very important to get acquainted with the environment and in the Getting Started section you’ll find some introductory activities to get yourself prepared for this course; particularly pay attention to the section on how to use Grasple.