Sequences, limits, and difference equations, Functions and their properties(1&2)

Difference Equations To Differential Equations: (Chap1&2)

Chapter 1: Sequences, limits, and difference equations

1.1 Calculus: Areas and tangents Download here

1.2 Sequences Download here

1.3 The sum of a sequence Download here

1.4Difference equations Download here

1.5 Nonlinear difference equations Download here

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Chapter 2: Functions and their properties

Functions and their graphs Download here

Trigonometric functions Download here

Limits and the notion of continuity Download here

Continuous functions Download here

Some consequences of continuity Download here

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Affine approximation and Integration D(3&4)

Chapter 3: Best affine approximations

3.1 Best affine approximations Download here

3.2 Best affine approximations, derivatives, and rates of change Download here

3.3 Differentiation of polynomials and rational functions Download here

3.4 Differentiation of compositions of functions Download here

3.5 Differentiation of trigonometric functions Download here

3.6 Newton’s method Download here

3.7 Rolle’s Theorem and the Mean Value Theorem Download here

3.8 Finding maximum and minimum values Download here

3.9The geometry of graphs Download here

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Chapter 4: Integration

4.1 The definite integral Download here

4.2 Numerical approximations of definite integrals Download here

4.3 The fundamental theorem of calculus Download here

4.4Using the fundamental theorem Download here

4.5 More techniques of integration Download here

4.6 Improper integrals Download here

4.7 More on area Download here

4.8 Distance, position, and the length of curves Download here

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Polynomial app transdantel function chap5&6

Chapter 5: Polynomial approximations and Taylor series

5.1Polynomial approximations Download here

5.2Taylor’s theorem Download here

5.3Infinite series revisited Download here

5.4Infinite series: the comparison test Download here

5.5Infinite series: the ratio test Download here

5.6Infinite series: absolute convergence Download here

5.7Power series Download here

5.8Taylor series Download here

5.9Some limit calculations Download here

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Chapter 6: More transcendental functions

6.1The exponential function Download here

6.2The natural logarithm function Download here

6.3Models of growth and decay Download here

6.4Integration of rational functions Download here

6.5Inverse trigonometric functions Download here

6.6Trigonometric substitutions Download here

6.7Hyperbolic functions Download here

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Complex and differential equations 7&8

Chapter 7: The complex plane

7.1 The algebra of complex numbers Download here

7.2 The calculus of complex functions Download here

7.3 Complex-valued functions: motion in the plane Download here

7.4 The two-body problem Download here

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Chapter 8: Differential equations

8.1Numerical solutions of differential equations Download here

8.2 Separation of variables Download here

8.3 First order linear differential equations Download here

8.4 Second order linear differential equations Download here

8.5 Applications: pendulums and mass-spring systems Download here

8.6 The geometry of solutions: the phase plane Download here

8.7 Power series solutions Download here

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