# Engineering Mathematics

- Author:
- Hisham Amir

This is a compiled book of worksheets to help students have a better understanding of engineering mathematics

## Table of Contents

### Algebra

- Basic Algebra Terms
- Polynomials
- Proof: Difference of two squares
- Proof: Perfect Square Trinomials
- Sum And Difference of 2 Cubes
- Guided Example: Multiplying Binomials
- Example: Factorising Polynomials
- Summary Practice: Factorising Polynomials
- Guided Example: Solving Quadratic Equations using Factorization
- Quiz: Solving Quadratic Equations by factorising.
- Solving Quadratic Equations using Quadratic Formula
- Multiply and Division of Fractions
- Practice: Addition and Substraction of Algebraic Fractions Ex1
- Exercise: Simplify Complex Fractions

### Law of Indices

- Indices
- Product of Powers Law
- Power of a power law
- Division of Powers Law
- Solving Equations Involving Indices
- Practice with steps: Indices Equation types Ex 1
- Practice with Steps: Indices Equation Types Ex2
- Practice with steps: Indices Equation Types Ex3
- Practice with steps: Solving Indices Equation types Ex4
- Practice with steps:Solving Indices Equation types Ex 5

### Laws of Logarithms

- Law of Logarithms
- Using Logarithm laws to solve equations
- Practice with steps: Solving Log Eqns (Product/Quotient law)
- Practice with steps: Solving Log Eqns (Law of Powers)
- Practice with steps: Log Eqns LvL 2 (quotient)
- Practice with steps: Solve Log Eqn LvL 2 (product)
- Practice with steps: Log Eqns LvL 3 (more than one law)
- Practice with Steps: Log Eqns LvL 4 (Multiple Laws)
- Practice: Solving Logarithmic Equations Lvl 5

### Binomial Theorem

### Using of straight line graphs

- Graph Equations
- Variables
- Identifying variables
- Graph of a Straight Line
- Gradient of a Straight Line
- The Y Intercept
- Vertical Line Graph
- Drawing a Graph using known equations
- Drawing a Straight Line Graph using known points
- Reading from the graph
- Lets do some practice
- Let's Do Some Practice
- Let's Do Some Practice

### Determinants

- Finding Determinants of a 2 x 2 matrix
- Determinant of a 2 x 2 Matrix
- Determinant of a 3 x 3 Matrix
- Step By Step: Finding determinant of 3 x 3 Matrix
- Step by Step: Finding determinant of a 3 x 3 Matrix
- Using Cramer's Rule(Matrices) to Solve Linear Equations
- Solving Simultaneous Equations (2 Unknowns)
- Practice: Solving Simultaneous Eqn (2 Unknowns)
- Using Determinants to solve Simultaneous Equations (3 Unknowns)
- Solving Simultaneous Equations (3 unknowns)
- Practice: Solve Simultaneous Equations (3 unknowns) LvL 1
- Practice: Solve Simultaneous Equations (3 unknowns) LvL 2

### Trigonometry

- Definitions used in Trigonometry
- Proof: Pythagora's Theorem
- Proof: Law of Sines
- Exercise: Using Sine Rule Ex 1
- Exercise: Using Sine Rule Ex 2
- Proof: Law of Cosines
- Introduction: Radians
- Convert Radians to Degrees
- Basic Trig Functions of the Unit Circle
- Values of points on the Unit Circle
- CAST Rule
- Explore the Sine Function
- Explore the Cosine Function
- The Sine, Cosine, Tangent and the Unit Circle
- The Pythagorean Identities
- Trigonometric Identity Explorer
- Proving Trigonometric Identities
- Solving Trigonometric Equations
- Deducing the Relationship: A sin x + B sin x= R cos (x+a)
- Asin(wt)+Bcos(wt)=Rsin(wt+a)
- Solving Trigonometric Equations in Harmonic Form
- Practice: Solve Trig Eqn in form of Acosx-Bsinx=C
- Practice: Solve Trig Eqns in form of Asinx-Bcos=C

### Vectors

- Intoduction: Vectors
- Explore:Vectors
- Unit Vectors
- Vectors: Addition and Subtraction (Graphically)
- Vectors: Algebraic Representation
- Exercise: Vectors, Algebraic Representation
- Exercise: Vector Exercise Including Scalar Product
- Dot And Cross Products
- Explore: Dot Product
- 3 Dimensional Vectors
- Explore: Cross Product

### Differentiation

- What is Differentiation
- Differentiation Concepts
- Practice: Standard Derivatives
- Practice: Standard Derivative Ex 2
- Practice: Differentiation of Polynomials
- The Product Rule
- Product Rule Calculator with steps
- Introduction: Quotient Rule
- Practice: Quotient Rule
- Practice: Quotient Rule Ex 2
- Practice: Quotient Rule Ex 3
- Practice: Quotient Rule Ex 4
- The Chain Rule
- Step by Step: Chain Rule
- Practice: chain rule
- Second Order Derivatives
- Practice: 2nd Order Derivatives
- Implicit Differentiation

### Integration

- Introduction to integration
- Practice: Integration Basics
- Practice: Integration Basics Lvl 2
- Practice: Integration Basics LvL 3
- Practice: Integration Basics LvL 4
- Practice: Integration Basics LvL 5
- Practice: Integration Basics LvL 6
- Practice: Integration Basics LvL 7
- Practice: Integration Basics LvL 8
- Practice: Integration Basics LvL 9
- Practice: integrate exponentials
- Introduction: Definite Integrals
- Practice: Definite Integral
- Practice: Definite Integral LvL 2
- Practice: Definite Integral LvL 3
- Practice: Definite Integral LvL 4
- Definite Integral Calculator

### Additional topics