Mathematics — C-Level
Eleven advanced chapters — from complex numbers and solid geometry through the methods and applications of integration.
Chapter 1
Complex Numbers
The new number system — complex numbers, their operations, trigonometric form, and roots.
Chapter 2
Mathematical Induction
The principle of mathematical induction, and using it to prove summation, divisibility, and inequality statements.
Chapter 3
Analytic Solid Geometry
The line, the plane, and the sphere in three-dimensional coordinate space.
Chapter 4
Vectors in Three Dimensions
The scalar (dot) product, the vector (cross) product, and lines and planes in 3D expressed with vectors.
Chapter 5
Permutation and Combination
Counting techniques — permutations and combinations — and their applications across mathematics, statistics, science, and engineering.
Chapter 6
Circles and Parabolas
Conic sections, the general equations of circles and parabolas, and translation and rotation of axes.
Chapter 7
Trigonometric Functions and Their Graphs
Graphs of the trigonometric functions and their transformations, inverse trigonometric functions, and differentiation of trigonometric functions.
Chapter 8
Logarithmic and Exponential Functions
Graphs of logarithmic and exponential functions, their transformations, and their derivatives.
Chapter 9
Applications of Derivatives
Critical points, maxima and minima, the second derivative test, and linear approximation.
Chapter 10
Methods of Integration
Basic integration, the substitution method, integration by parts, and the partial fraction method.
Chapter 11
Applications of Integration
The definite integral as area under a curve, area between two curves, and volumes of revolution.