Program of the 2E1 Course

Multivariable Functions and Partial Derivatives Ref(1)
Week  1
Lecture   1. Review of Derivatives in the calculus of a single variable
Lecture   2. Review of Integrals in the calculus of a single variable
Week  2
Lecture   3. Functions and variables
Lecture   4. Level curves & Graphing
Week  3
Lecture   5. Limits and continuity.
Lecture   6. Definition and Notation and examples of Partial Derivatives
Week  4
Lecture   7. Examples on second order Partial Derivatives
Lecture   8. Euler's Theorem
Week  5
Lecture   9. Standard Linear Approximation. Lecture
Lecture 10. Differentials and the Sensitivity to change. The chain rule
Week  6
Lecture 11.
Taylor's Formula and the second derivative test. Formula
Lecture 12. Directional Derivatives Lecture
Week 7
Lecture 13.
Maxima, Minima and Saddle points. Lecture
Lecture 14. Lagrange Multipliers. Exercises

Multiple Integrals. Ref(2)

Week 8
Lecture 15.  Double Integrals. Definitions.
Lecture 16.  Double Integrals. Limits of Integration. Week 9
Lecture 17.  Areas and Center of Mass. Lecture
Lecture 18.  First and Second Moment. Lecture
Week 10
Lecture 19.
Double Integrals in Polar form Lecture
Lecture 20.
Triple integrals in Rectangular Coordinates. Lecture
Week 11
Lecture 21.  Triple Integrals in Cylindrical and Spherical Coordinates. Lecture
Lecture 22.  Change of Variable on Multiple integrals: The Jacobian. Lecture

Linear Algebra: Eigenvectors and Eigenvalues
. Ref(3)

Week 12
Lecture 23.  Review of Vectors and Matrices Lecture
Lecture 24.  Linear Combinations and Linear Vector Spaces Lecture
Week 13
Lecture 25.  Examples of Vector Spaces Lecture

Lecture 26.  Subspaces  Lecture
Week 14
Lecture 27.
Span of a Vectors Space Lecture
Lecture 28.
Linear Dependence and Linear Independence Lecture
Week 15
Lecture 29.
Basis Lecture
Lecture 30.  Dimension of a Space. Row Space, Column Space & Null Space Lecture
Week 16

Lecture 31.  NullSpace Basis, Row Space Basis & Column Space Basis. Lectures

Lecture 32. Rank and Nullity Lecture
Week 17
Lecture 33.
Inner Product Space Lecture
Lecture 34. Angle between vectors, Gram-Schmidt Process Lecture
Week 18
Lecture 35.  Least Square Method, Orthogonal Matrices, Change of Variable Lecture

Lecture 36. Eigenvalues and Eigenvectors. Lecture

Fourier Analysis. Ref(4)

Week 19
Lecture 37. Periodic Functions, Trigonometric Series, Fourier Series
Lecture 38. Functions of any period p=2L
Week 20
Lecture 39. Even and Odd Functions. Half Range Expantion.
Lecture 40. Forced Oscillations, Examples
Week 21
Lecture 41. Fourier Transform
Lecture 42. Examples.
Week 22
Lecture 43. Examination Review
Lecture 44. Examination Review

References:
1.Stewart – Calculus, Concepts & Contexts, -Ed. Thomson- (To understand the theory)
2.Cole and Clegg, Complete Solution Manual for Stewart Calculus,-Ed. Thomson- (To understand how to solve the probems)
3.Thomas 10th Ed: ch. 11 (Multivariable Calculus).

4.Thomas 10th Ed: ch. 12 (Multiple Integrals).

5.Anton & Rorres 7th Ed: ch 5, 6 and7 (General vector spaces, Spaces with Inner product, Eigenvalue and eigenvectors)
4. Kreyszig 8th Ed: ch 10 (Fourier Series) except sections10.7 and 10.9