Mathematics for Physicists

Mathematics as the language for physics......Page 11
The product of two powers......Page 13
Exponential Function......Page 14
The Logarithmic Function......Page 15
Trigonometric functions......Page 16
Trigonometric identities......Page 18
Inverse Trig Functions......Page 20
Polar Coordinates......Page 21
Polar curves......Page 22
What is a vector?......Page 25
Negative of a vector......Page 26
Triangle Law......Page 27
Associativity......Page 28
Components in 2 dimensions......Page 29
Sum and Difference of vectors in Component Form......Page 30
Scaling of Vector......Page 31
The scalar or dot product......Page 32
Component form of dot product......Page 33
Work......Page 34
The vector product......Page 35
*triple products*......Page 36
Some physical examples......Page 37
Standard form of L......Page 38
Differential of a sum......Page 41
Function of a function (chain rule)......Page 42
Differential of inverse function......Page 43
Implicit Differentiation......Page 44
Differentiation of parametric equations......Page 45
Vector functions......Page 46
Polar curves......Page 47
Partial derivatives......Page 48
Multiple partial derivatives......Page 51
Application of differentiation: Calculation of small errors......Page 52
Inverse of differentiation......Page 53
Strategy......Page 54
Type 1......Page 55
Type 2......Page 56
Integration by Parts......Page 57
Integrals of the form I=(px+q)/(x2+ax+b) d x......Page 59
Completing the Square......Page 60
Partial fractions......Page 61
Integrals with square roots in denominator......Page 64
Area between two curves......Page 67
Basic Derivation of Area Formula......Page 68
Volumes of Revolution......Page 69
First moment of the area about the y axis......Page 70
First Moment of the area about the x axis......Page 72
Centroid of a plane area......Page 73
Second Moment of Area......Page 74
introduction......Page 75
Separable type......Page 76
linear type......Page 78
Homogeneous Type......Page 79
Bernoulli's Equation......Page 81