18.013A | Spring 2005 | Undergraduate

Calculus with Applications


This course is designed as a self-study program in differential calculus. The content is organized into “chapters” below.

chapter # Topics

0 The Spreadsheet
1 Philosophy, Numbers and Functions
2 The Exponential Function and Trigonometric Functions
3 Vectors, Dot Products, Matrix Multiplication and Distance
4 Area of a Parallelogram, Determinants, Volume and Hypervolume, the Vector Product
5 Vectors and Geometry in Two and Three Dimensions
6 Differentiable Functions, the Derivative and Differentials
7 Computation of Derivatives from their Definition
8 Calculation of Derivatives by Rule
9 Derivatives of Vector Fields and the Gradient in Polar Coordinates
10 Higher Derivatives, Taylor Series, Quadratic Approximations and Accuracy of Approximations
11 Quadratic Approximations in Several Dimensions
12 Applications of Differentiation: Direct Use of Linear Approximation
13 Solving Equations
14 Extrema
15 Curves
16 Some Important Examples and a Formulation in Physics
17 The Product Rule and Differentiating Vectors
18 Complex Numbers and Functions of Them
19 The Anti-derivative or Indefinite Integral
20 The Area under a Curve and its Many Generalizations
21 The Fundamental Theorem of Calculus in One Dimension
22 The Fundamental Theorem of Calculus in Higher Dimensions; Additive Measures, Stokes Theorem and the Divergence Theorem
23 Reducing a Line Integral to an Ordinary Integral and Related Reductions
24 Reducing a Surface Integral to a Multiple Integral and the Jacobian
25 Numerical Integration
26 Numerical Solution of Differential Equations
27 Doing Integrals
28 Introduction to Electric and Magnetic Fields
29 Magnetic Fields, Magnetic Induction and Electrodynamics
30 Series
31 Doing Area, Surface and Volume Integrals
32 Some Linear Algebra
33 Second Order Differential Equations

Course Info

As Taught In
Spring 2005
Learning Resource Types
Online Textbook