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Calculus with Applications >> Content Detail



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


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

 








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