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College Mathematics Syllabus C consists of 2 volumes (College Mathematics 1 and College Mathematics 2) and is a two-year series for 11th and 12th grades. Students in and out of schools can make good use of these books for self study.  These two volumes provide a fundamental background knowledge of Mathematics for other College and University courses such as Physical and Biological Sciences, Computer Science, Economics, Management and Social Science, Statistics, Accountancy and Business Studies.  

This series is deliberately comprehensive, brief and concise.  Theorems and definitions are emphasized and there are examples to illustrate each new concept presented and to show different computational techniques involved.  This direct approach allows students to grasp basic concepts and techniques clearly and quickly. 

Exercises form an integral part of the book.  They provide an opportunity for students to test their understanding of the concepts learnt and to acquire through practice, confidence in handling computational techniques.  Answers to problems are also included.

There are no workbooks nor teacher's guides for this college math series. The textbook provides answer keys to the Textbook Exercises.

 Algebra
 Complex Numbers
 Relations and Functions
 Trigonometry
 Vectors
 Matrices and Transformations
 Differential and Integral Calculus
 Probability and Statistics
 Kinematics, Dynamics and Statics

College Mathematics 2

1. Matrices and Transformations

• Matrices
• Square Matrices
• Equality of Matrices
• Transpose of a Matrix
• Addition of Matrices
• Null of Zero Matrices
• Subtraction of Matrices
• Multiplication of a Matrix by a Scalar
• Multiplication of Matrices
• Unit or Identity Matrices
• Inverse of a Square Matrix and Determinants
• Transformations
• Reflections
• Rotations
• Stretching Transformations
• Shear Transformations
• Inverse Transformations
• General Linear Transformations

2. The Derivative

• Gradient and Derivative
• The Derivative of xⁿ
• Differentiation of Sum, Difference, Product and Quotient
• Differentiation of Trigonometrical Functions
• The Chain Rule
• Implicit Differentiation
• Parametric Representation
• Exponential Functions
• Logarithmic Functions
• Differentiation of Exponential and Logarithmic Functions
• Inverse Trigonometric Functions
• Higher Derivatives

3. Applications of Differentiation

• Rates of Change
• Velocity and Acceleration
• Maxima and Minima
• Maximization and Minimization Problems
• Inflexion Points
• Graph Sketching
• Small Increments

4. The Indefinite Integral

• Introduction
• Definition of Indefinite Integral
• Significance of the Constant C
• Basic Properties of Indefinite Integral
• Method of Substitution
• Integration by Parts
• Partial Fractions

5. The Definite Integral

• Introduction
• Definite Integral as the Limit of a Sum
• Computation of Definite Integrals 
• Plane Areas
• Mean Value of a Function
• Volumes
• Trapezium Rule

6. Polar Coordinates, de Moivre's Theorem and Power Series

• Polar Coordinates
• Gradient of Tangent
• Curve Sketching
• Area
• Exponential Function and Some of its Properties
• Euler's Formula and de Moivre's Theorem
• Higher Order Differentiation
• Power Series Expansion
• MacLaurin's Theorem
• Taylor's Theorem 

7. Differential Equations

• Introduction
• Law of Growth and Decay
• Separable Equations
• Solution Curves
• Linear Equations
• Second Order Linear Equations
• Simple Harmonic Motion
• Inhomogeneous Equations
• Other Types of Second Order Differential Equations

8. Solutions of Algebraic Equations

• Introduction
• Location of Roots
• Estimates of Roots and Their Error
• Linear Interpolation
• The Newton-Raphson Method

9. Probability

• Random Experiments and Events
• Relative Frequency and Probability of an Event
• Finite Sample Spaces and Equally Likely Outcomes
• Conditional Probability and Independence
• Total Probability Theorem and Bayers' Theorem

10. Random Variables

• Random Variables
• Distribution Function and Expectation of a Random Variable
• Bivariate Random Variables

11. Some Important Classes of Distribution 

• Uniform Distribution (Discrete Type)
• Binomial Distribution
• Poisson Distribution
• Rectangular Distribution
• Normal Distribution
• Central Limit Theorem

12. Statistical Inference 

• Presentation of Observed Data
• Sample Characteristics I
• Sample Characteristics II
• Point and Interval Estimations
• Test of Hypotheses

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Samples

Chapter 9 Probability p.447 
Chapter 9 Probability p.448 
Chapter 9 Probability p.449

 

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