Notes and problem sets for practice

Difference Equations To Differential Equations: 

  This Section contains the notes and problem sets of Affine approximation and Integration  . Particularly,  the topics of the above two chapter's topics notes are given below:

Chapter 1: Sequences, limits, and difference equations
  Calculus: Areas and tangents,  Sequences,  The sum of a sequence, Difference equations, Nonlinear difference equations

Chapter 2: Functions and their properties
  Functions and their graphs, Trigonometric functions,
Limits and the notion of continuity, Continuous functions, Some consequences of continuity

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Affine approximation and Integration 

  This Section contains the notes and problem sets of Affine approximation and Integration  . Particularly,  the topics of the above two chapter's topics notes are given below:

Chapter 3: Best affine approximations
   Best affine approximations, Best affine approximations, derivatives, and rates of change,  Differentiation of polynomials and rational functions, Differentiation of compositions of functions, ifferentiation of trigonometric functions, Newton’s method,  Rolle’s Theorem and the Mean Value Theorem,  Finding maximum and minimum values , The geometry of graphs

Chapter 4: Integration
   The definite integral,  Numerical approximations of definite integrals, The fundamental theorem of calculus, Using the fundamental theorem, More techniques of integration,  Improper integrals,  More on area, Distance, position, and the length of curves
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Polynomial app transdantel function 

   This Section contains the notes and problem sets of Polynomial app transdantel function . Particularly,  the topics of the above two chapter's topics notes are given below:

Chapter 5: Polynomial approximations and Taylor series
  Polynomial approximations, Taylor’s theorem, Infinite series revisited, Infinite series: the comparison test, Infinite series: the ratio test, Infinite series: absolute convergence , Power series, Taylor series, Some limit calculations

Chapter 6: More transcendental functions

The exponential function, The natural logarithm function, Models of growth and decay, Integration of rational functions, Inverse trigonometric functions, Trigonometric substitutions, Hyperbolic functions
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Complex and differential equations 
   This chapter contains the notes and problem sets of Complex plane and Differential equations. Particularly,  the topics of the above two chapter's topics notes are given below:

Chapter 7: The complex plane
   The algebra of complex numbers,  The calculus of complex functions, Complex-valued functions: motion in the plane, The two-body problem

Chapter 8: Differential equations
   Numerical solutions of differential equations, Separation of variables, First order linear differential equations,  Second order linear differential equations, Applications: pendulums and mass-spring systems, The geometry of solutions: the phase plane, Power series solutions
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