Lecture notes12: Total differential, Tangent planes and normals

Lecture notes12: Total differential, Tangent planes and normals

34.

Gradient of a scaler field Download here
35.

Tangent plane and normal Download here

36.

Mean value theorem and Linearization Download here

Lecturer notes 11: Partial derivatives, Chain rules, Implicit differentiation, Gradient, Directional derivatives

Lecturer notes 11: Partial derivatives, Chain rules, Implicit differentiation, Gradient, Directional derivatives

31.

Partial derivatives Download here

32.

Chain rules Download here

33.

Implicit differentiation Download here

Lecturer notes 10 : Scaler fields, Limit and Continuity

Lecturer notes 10 :   Scaler fields, Limit and   Continuity

 28.

Series of functions   Download here

29.

 Limit of scaler fields Download here

30. 

Continuity of scaler fields   Download here

Lecture notes 8 : Applications of Integration - II

Lecture notes 8 :  Applications  of  Integration  - II 

22.

Arc  Length  of  a  Plane  Curve Download here

23.

Area of Surface of revolution Download here


24.

Volume  of  solids  of  revolution  by  washer  method Download here

Lecture notes 7 : Applications of Integration - I

Lecture notes 7  :  Applications  of  Integration  - I

19 . 

Definition  of  the  natural  logarithmic  function base Download here

20.

Definition of the power function and logarithmic function with positive base Download here

21.

Relative  rate  of  growth  of  functionsDownload here

Lecture notes-6 :Definition of Integral

Lecture notes-6 :Definition  of  Integral:

16. 

Integral  from  upper  and  lower  sums Download here

17. 

Fundamental theorem of calculus Download here

18. 

Approximating Integral : Trapezoidal Rule 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

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

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

Answer:View

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

Answers: View

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

Answer:View

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

Answer:View

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

Answers: View

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

Answers for selected problems are available  . View