FSc Part 1 - Mathematics
Mathematics-Algebra and Trigonometry is a compulsory subject for those intermediate students who opted for FSc Pre-Engineering or ICS. There are total 14 chapters in the book which are devised to make create logical and analytical skills learners. All chapters and their exercises will help students to identify and solve problems quickly and they will also equip them with time management skills.
1: Number Systems
Introduction - Rational numbers and irrational numbers - Properties of real numbers - Complex num...
2: Sets,Functions and Groups
Introduction - Operations on Sets - Venn Diagrams - Operations on Three Sets - Properties of Uni...
3: Matrices and Determinants
Introduction - Determinant of a 2×2 matrix - Solution of simultaneous linear equations by using ma...
4: Quadratic Equations
Introduction - Solutions of Equations Reducible to the Quadratic Equation - Three Cube Roots of Un...
5: Partial Fractions
Introduction - Rational Fraction - Resolution of a Rational Fraction P(x)/Q (x) into Partial Fract...
6: Sequences and Series
Introduction - Types of Sequences - Arithmetic Progression(A.P) - Aritmetic Mean (A.M) - Series...
7: Permutation,Combination and Probability
Introduction - Permutation - Combinations - Probability
8: Mathematical Inductions and Binomial Theorem
Introduction - Principle of Mathematical Induction - Principle of Extended Mathematical Induction ...
9: Fundamentals of Trigonometry
Introduction - Principle of Mathematical Induction - Principle of Extended Mathematical Induction...
10: Trigonometric Identities Sum and Difference of Angles
Introduction - Deductions from Fundamental Law - Trigonometric Ratios of Allied Angles - Further ...
11: Trigonometric Functions and their Graphs
Introduction - Period of Trigonometric Functions - Values of Trigonometric Functions - Graphs of ...
12: Application of Trigonometry
Introduction - Tables of Trigonometric Ratios - Solution of Right Triangles - Heights and Distan...
13: Inverse Trigonometric Functions
Introduction - The Inverse Sine Function - The Inverse Cosine Function - The Inverse Tangent Func...
14: Solutions of Trigonometric Equations
Introduction - Solution of General Trigonometric Equations
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- Number System
In this chapter, students will learn about rational and irrational numbers, real numbers and their properties and complex numbers. Students will also revise the concept of a real line.
- Sets, Functions and Groups
The second chapter will cover elements such as set and its operations, Venn diagrams, inductive logic, deductive logic, inverse function and its reverse law.
- Matrices and Determinants
Students will learn matrices, determinants and their applications in this lesson. They will study different types of matrices and their solutions; will learn that how linear equations could be solved so easily with the help of matrices.
- Quadratic Equations
Students will come to know about equations reducible to the quadratic equation, 3 cube roots of unity and 4 fourth roots of unity. They will also study polynomial functions and system of equations involving two variables.
- Partial Fractions
The 5th chapter will address rational fractions and their resolution into partial fractions.
- Sequences and Series
Students will cover topics such as arithmetic progression and mean series, disadvantages of AP, geometric means and series, harmonic progressions in this chapter.
- Permutation , Combination and Probability
This lesson will cover applications of permutation, combination and probability.
- Mathematical Induction and Binomial Theorem
You will study mathematical and extended methodical inductions and binomial theorem in this chapter.
- Fundamentals of Trigonometry
This chapter will teach the measurement of angles, the relation between an arc of a circle and central angle and trigonometric function of various angles.
- Trigonometric Identities
You will study that how trigonometric identities can be used to find the value of any angle. It will also discuss basic mathematical operations of sines and cosines.
- Trigonometric Functions and their Graphs
This chapter will elaborate trigonometric functions and their representation on a graph.
- Application of Trigonometry
Students will learn the solution of triangle using trigonometry and they will also study the applications and usage of this branch of mathematics.
- Inverse Trigonometric Functions
You will learn inverse functions of Cosine, Sine, tangent, cotangent, secant and cosecant. They will also study about the range and domain of these functions.
- Solutions of Trigonometric Equation
The last chapter of the book deals with trigonometric equations and their solution.