1. Complex Numbers…………………………………………………………………………. 7
1.1 Introduction to Complex Numbers
1.2 Rectangular, Polar and Exponential forms of a complex numbers
1.3 De-Moivre’s Theorem
1.4 Power, Root and Logarithm of Complex number
1.5 Trigonometric, Exponential and Hyperbolic Functions
1.6 Applications of Complex Numbers in Physics
Numerical Problems
2. Partial Differentiation………………………………………………………………….. 43
2.1 Introduction of Partial Differentiation
2.2 Successive, Total and Exact Differentiation
2.3 Chain Rule
2.4 Theorems of Differentiation
2.5 Implicit and explicit functions
2.6 Applications of Partial differentiation in Physics Numerical Problems
3. Scalar and Vector Algebra…………………………………………………………….. 83
3.1 Introduction to Scalars and Vectors
3.2 Scalar and Vector product of two vectors
3.3 Scalar Triple Product
3.4 Vector Triple Product
3.5 Scalar and Vector Fields
3.6 Laplacian operator
3.7 Gradient of Scalar field and its physical significance
3.8 Divergence of scalar field and its physical significance
3.9 Curl of vector field and its significance
3.10 Vector Identities
Numerical Problems