Lecture Notes 5 : Linear and Quadratic  Approximations, Error  Estimates,  Taylor's Theorem,  Newton and Picard Methods

13.

Linear Approximations 
Download here
14. 

Taylor's  Theorem Download here
15. 

Newton's  method  Download here 

Lecturer notes-4 : Local / Global Maximum / Minimum and Curve Sketching

Lecturer notes-4  :  Local  /  Global  Maximum  /  Minimum  and   Curve  Sketching 

Lecture  10  :  Sufficient  conditions  for  increasing  /  decreasingDownload here

Lecture  11  :  Absolute  Maximum  /  Minimum 
Download here

Lecture 12 : Asymptoes
Download here

Lecturer notes-3 : Differentiation and Mean Value Theorems:

Lecturer notes-3 : Differentiation  and  Mean  Value   Theorems:

7.

Differentiation Download here


8.

Chain  Rule  Download here


9.

Roll's theorem and Mean Value Theorem Download here

Lecturer notes-2 Limits and Continuity of Functions:

Lecturer notes-2 Limits  and  Continuity  of   Functions:


4.

Limit  at  a  point Download here


5.

 ContinuityDownload here


6.

Properties of Continuous Functions Download here 

Lecturer notes:1 Real Numbers, Functions and Sequences

 Real  Numbers,  Functions  and  Sequences 

1.Real  Numbers,  Functions  Download here  


2. Convergent  &  Bounded  SequencesDownload here


3.Monotone  Sequence  and  Limit  theoremDownload here

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

For more Visit here


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
For more Click here for download

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
For moreClick here to download


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
For more Click here for download

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

Answer page is in view format only, not in format of download View

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

Answer page is in view format only, not in format of download View