Engineering Mathematics

Hisham Amir, 13. 10. 2015

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

Obsah

  1. Algebra
    1. Basic Algebra Terms
    2. Polynomials
    3. Proof: Difference of two squares
    4. Proof: Perfect Square Trinomials
    5. Sum And Difference of 2 Cubes
    6. Guided Example: Multiplying Binomials
    7. Example: Factorising Polynomials
    8. Summary Practice: Factorising Polynomials
    9. Guided Example: Solving Quadratic Equations using Factorization
    10. Quiz: Solving Quadratic Equations by factorising.
    11. Solving Quadratic Equations using Quadratic Formula
    12. Multiply and Division of Fractions
    13. Practice: Addition and Substraction of Algebraic Fractions Ex1
    14. Exercise: Simplify Complex Fractions
  2. Law of Indices
    1. Indices
    2. Product of Powers Law
    3. Power of a power law
    4. Division of Powers Law
    5. Solving Equations Involving Indices
    6. Practice with steps: Indices Equation types Ex 1
    7. Practice with Steps: Indices Equation Types Ex2
    8. Practice with steps: Indices Equation Types Ex3
    9. Practice with steps: Solving Indices Equation types Ex4
    10. Practice with steps:Solving Indices Equation types Ex 5
  3. Laws of Logarithms
    1. Law of Logarithms
    2. Using Logarithm laws to solve equations
    3. Practice with steps: Solving Log Eqns (Product/Quotient law)
    4. Practice with steps: Solving Log Eqns (Law of Powers)
    5. Practice with steps: Log Eqns LvL 2 (quotient)
    6. Practice with steps: Solve Log Eqn LvL 2 (product)
    7. Practice with steps: Log Eqns LvL 3 (more than one law)
    8. Practice with Steps: Log Eqns LvL 4 (Multiple Laws)
    9. Practice: Solving Logarithmic Equations Lvl 5
  4. Binomial Theorem
    1. Simplify Factorials
    2. Binomial Expansion
    3. Practice: Binomial Expansion Ex 1
    4. Practice: Binomial Expansion Ex 2
    5. Binomial Expansion (Negative Power)
    6. Binomial Expansion - Fractional Power
  5. Using of straight line graphs
    1. Graph Equations
    2. Variables
    3. Identifying variables
    4. Graph of a Straight Line
    5. Gradient of a Straight Line
    6. The Y Intercept
    7. Vertical Line Graph
    8. Drawing a Graph using known equations
    9. Drawing a Straight Line Graph using known points
    10. Reading from the graph
    11. Lets do some practice
    12. Let's Do Some Practice
    13. Let's Do Some Practice
  6. Determinants
    1. Finding Determinants of a 2 x 2 matrix
    2. Determinant of a 2 x 2 Matrix
    3. Determinant of a 3 x 3 Matrix
    4. Step By Step: Finding determinant of 3 x 3 Matrix
    5. Step by Step: Finding determinant of a 3 x 3 Matrix
    6. Using Cramer's Rule(Matrices) to Solve Linear Equations
    7. Solving Simultaneous Equations (2 Unknowns)
    8. Practice: Solving Simultaneous Eqn (2 Unknowns)
    9. Using Determinants to solve Simultaneous Equations (3 Unknowns)
    10. Solving Simultaneous Equations (3 unknowns)
    11. Practice: Solve Simultaneous Equations (3 unknowns) LvL 1
    12. Practice: Solve Simultaneous Equations (3 unknowns) LvL 2
  7. Trigonometry
    1. Definitions used in Trigonometry
    2. Proof: Pythagora's Theorem
    3. Proof: Law of Sines
    4. Exercise: Using Sine Rule Ex 1
    5. Exercise: Using Sine Rule Ex 2
    6. Proof: Law of Cosines
    7. Introduction: Radians
    8. Convert Radians to Degrees
    9. Basic Trig Functions of the Unit Circle
    10. Values of points on the Unit Circle
    11. CAST Rule
    12. Explore the Sine Function
    13. Explore the Cosine Function
    14. The Sine, Cosine, Tangent and the Unit Circle
    15. The Pythagorean Identities
    16. Trigonometric Identity Explorer
    17. Proving Trigonometric Identities
    18. Solving Trigonometric Equations
    19. Deducing the Relationship: A sin x + B sin x= R cos (x+a)
    20. Asin(wt)+Bcos(wt)=Rsin(wt+a)
    21. Solving Trigonometric Equations in Harmonic Form
    22. Practice: Solve Trig Eqn in form of Acosx-Bsinx=C
    23. Practice: Solve Trig Eqns in form of Asinx-Bcos=C
  8. Vectors
    1. Intoduction: Vectors
    2. Explore:Vectors
    3. Unit Vectors
    4. Vectors: Addition and Subtraction (Graphically)
    5. Vectors: Algebraic Representation
    6. Exercise: Vectors, Algebraic Representation
    7. Exercise: Vector Exercise Including Scalar Product
    8. Dot And Cross Products
    9. Explore: Dot Product
    10. 3 Dimensional Vectors
    11. Explore: Cross Product
  9. Differentiation
    1. What is Differentiation
    2. Differentiation Concepts
    3. Practice: Standard Derivatives
    4. Practice: Standard Derivative Ex 2
    5. Practice: Differentiation of Polynomials
    6. The Product Rule
    7. Product Rule Calculator with steps
    8. Introduction: Quotient Rule
    9. Practice: Quotient Rule
    10. Practice: Quotient Rule Ex 2
    11. Practice: Quotient Rule Ex 3
    12. Practice: Quotient Rule Ex 4
    13. The Chain Rule
    14. Step by Step: Chain Rule
    15. Practice: chain rule
    16. Second Order Derivatives
    17. Practice: 2nd Order Derivatives
    18. Implicit Differentiation
  10. Integration
    1. Introduction to integration
    2. Practice: Integration Basics
    3. Practice: Integration Basics Lvl 2
    4. Practice: Integration Basics LvL 3
    5. Practice: Integration Basics LvL 4
    6. Practice: Integration Basics LvL 5
    7. Practice: Integration Basics LvL 6
    8. Practice: Integration Basics LvL 7
    9. Practice: Integration Basics LvL 8
    10. Practice: Integration Basics LvL 9
    11. Practice: integrate exponentials
    12. Introduction: Definite Integrals
    13. Practice: Definite Integral
    14. Practice: Definite Integral LvL 2
    15. Practice: Definite Integral LvL 3
    16. Practice: Definite Integral LvL 4
    17. Definite Integral Calculator
  11. Additional topics
    1. Prime Factorization

1.

Algebra

  • 1. Basic Algebra Terms
  • 2. Polynomials
  • 3. Proof: Difference of two squares
  • 4. Proof: Perfect Square Trinomials
  • 5. Sum And Difference of 2 Cubes
  • 6. Guided Example: Multiplying Binomials
  • 7. Example: Factorising Polynomials
  • 8. Summary Practice: Factorising Polynomials
  • 9. Guided Example: Solving Quadratic Equations using Factorization
  • 10. Quiz: Solving Quadratic Equations by factorising.
  • 11. Solving Quadratic Equations using Quadratic Formula
  • 12. Multiply and Division of Fractions
  • 13. Practice: Addition and Substraction of Algebraic Fractions Ex1
  • 14. Exercise: Simplify Complex Fractions

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2.

Law of Indices

Chapter on the various laws of indices

  • 1. Indices
  • 2. Product of Powers Law
  • 3. Power of a power law
  • 4. Division of Powers Law
  • 5. Solving Equations Involving Indices
  • 6. Practice with steps: Indices Equation types Ex 1
  • 7. Practice with Steps: Indices Equation Types Ex2
  • 8. Practice with steps: Indices Equation Types Ex3
  • 9. Practice with steps: Solving Indices Equation types Ex4
  • 10. Practice with steps:Solving Indices Equation types Ex 5

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Laws of Logarithms

Chapter on the various laws of Logarithms

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

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Binomial Theorem

Chapter to help better understand the Binomial Theorem

  • 1. Simplify Factorials
  • 2. Binomial Expansion
  • 3. Practice: Binomial Expansion Ex 1
  • 4. Practice: Binomial Expansion Ex 2
  • 5. Binomial Expansion (Negative Power)
  • 6. Binomial Expansion - Fractional Power

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Using of straight line graphs

Use straight line graph to verify the law connecting two variables

  • 1. Graph Equations
  • 2. Variables
  • 3. Identifying variables
  • 4. Graph of a Straight Line
  • 5. Gradient of a Straight Line
  • 6. The Y Intercept
  • 7. Vertical Line Graph
  • 8. Drawing a Graph using known equations
  • 9. Drawing a Straight Line Graph using known points
  • 10. Reading from the graph
  • 11. Lets do some practice
  • 12. Let's Do Some Practice
  • 13. Let's Do Some Practice

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Determinants

  • 1. Finding Determinants of a 2 x 2 matrix
  • 2. Determinant of a 2 x 2 Matrix
  • 3. Determinant of a 3 x 3 Matrix
  • 4. Step By Step: Finding determinant of 3 x 3 Matrix
  • 5. Step by Step: Finding determinant of a 3 x 3 Matrix
  • 6. Using Cramer's Rule(Matrices) to Solve Linear Equations
  • 7. Solving Simultaneous Equations (2 Unknowns)
  • 8. Practice: Solving Simultaneous Eqn (2 Unknowns)
  • 9. Using Determinants to solve Simultaneous Equations (3 Unknowns)
  • 10. Solving Simultaneous Equations (3 unknowns)
  • 11. Practice: Solve Simultaneous Equations (3 unknowns) LvL 1
  • 12. Practice: Solve Simultaneous Equations (3 unknowns) LvL 2

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Trigonometry

Chapter on Trigonometry

  • 1. Definitions used in Trigonometry
  • 2. Proof: Pythagora's Theorem
  • 3. Proof: Law of Sines
  • 4. Exercise: Using Sine Rule Ex 1
  • 5. Exercise: Using Sine Rule Ex 2
  • 6. Proof: Law of Cosines
  • 7. Introduction: Radians
  • 8. Convert Radians to Degrees
  • 9. Basic Trig Functions of the Unit Circle
  • 10. Values of points on the Unit Circle
  • 11. CAST Rule
  • 12. Explore the Sine Function
  • 13. Explore the Cosine Function
  • 14. The Sine, Cosine, Tangent and the Unit Circle
  • 15. The Pythagorean Identities
  • 16. Trigonometric Identity Explorer
  • 17. Proving Trigonometric Identities
  • 18. Solving Trigonometric Equations
  • 19. Deducing the Relationship: A sin x + B sin x= R cos (x+a)
  • 20. Asin(wt)+Bcos(wt)=Rsin(wt+a)
  • 21. Solving Trigonometric Equations in Harmonic Form
  • 22. Practice: Solve Trig Eqn in form of Acosx-Bsinx=C
  • 23. Practice: Solve Trig Eqns in form of Asinx-Bcos=C

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Vectors

  • 1. Intoduction: Vectors
  • 2. Explore:Vectors
  • 3. Unit Vectors
  • 4. Vectors: Addition and Subtraction (Graphically)
  • 5. Vectors: Algebraic Representation
  • 6. Exercise: Vectors, Algebraic Representation
  • 7. Exercise: Vector Exercise Including Scalar Product
  • 8. Dot And Cross Products
  • 9. Explore: Dot Product
  • 10. 3 Dimensional Vectors
  • 11. Explore: Cross Product

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Differentiation

Chapter on Differentiation

  • 1. What is Differentiation
  • 2. Differentiation Concepts
  • 3. Practice: Standard Derivatives
  • 4. Practice: Standard Derivative Ex 2
  • 5. Practice: Differentiation of Polynomials
  • 6. The Product Rule
  • 7. Product Rule Calculator with steps
  • 8. Introduction: Quotient Rule
  • 9. Practice: Quotient Rule
  • 10. Practice: Quotient Rule Ex 2
  • 11. Practice: Quotient Rule Ex 3
  • 12. Practice: Quotient Rule Ex 4
  • 13. The Chain Rule
  • 14. Step by Step: Chain Rule
  • 15. Practice: chain rule
  • 16. Second Order Derivatives
  • 17. Practice: 2nd Order Derivatives
  • 18. Implicit Differentiation

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Integration

Chapter on Integration

  • 1. Introduction to integration
  • 2. Practice: Integration Basics
  • 3. Practice: Integration Basics Lvl 2
  • 4. Practice: Integration Basics LvL 3
  • 5. Practice: Integration Basics LvL 4
  • 6. Practice: Integration Basics LvL 5
  • 7. Practice: Integration Basics LvL 6
  • 8. Practice: Integration Basics LvL 7
  • 9. Practice: Integration Basics LvL 8
  • 10. Practice: Integration Basics LvL 9
  • 11. Practice: integrate exponentials
  • 12. Introduction: Definite Integrals
  • 13. Practice: Definite Integral
  • 14. Practice: Definite Integral LvL 2
  • 15. Practice: Definite Integral LvL 3
  • 16. Practice: Definite Integral LvL 4
  • 17. Definite Integral Calculator

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Additional topics

Additional topics to supplement your maths foundation

  • 1. Prime Factorization

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Informace