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Foundation Further Mathematics

54 lessons across 11 topics

1. Topic 1(COLON) Mathematical Proof and Reasoning

1Lesson 1.1: The Language Of Mathematical Argument2Lesson 1.2: Direct Proof, Contradiction And Counter-example3Lesson 1.3: Proof By Mathematical Induction: Series And Divisibility4Lesson 1.4: Induction With Sequences, Inequalities And Matrices

2. Topic 2(COLON) Algebra, Functions and Their Graphs

5Lesson 2.1: Polynomials, The Factor And Remainder Theorems6Lesson 2.2: Roots Of Polynomial Equations7Lesson 2.3: Partial Fractions And Algebraic Fractions8Lesson 2.4: The Modulus Function And Inequalities9Lesson 2.5: Rational Functions, Asymptotes And Curve Sketching10Lesson 2.6: Functions, Composition And Inverses

3. Topic 3(COLON) Sequences, Series and Summation

11Lesson 3.1: Standard Summation Formulae12Lesson 3.2: The Method Of Differences And Telescoping Sums13Lesson 3.3: Arithmetic And Geometric Series; Convergence14Lesson 3.4: The Binomial Expansion For Any Rational Index

4. Topic 4(COLON) Matrices and Linear Systems

15Lesson 4.1: Matrix Arithmetic16Lesson 4.3: Matrices As Linear Transformations17Lesson 4.4: Solving Systems Of Linear Equations18Lesson 4.5: Eigenvalues And Eigenvectors

5. Topic 5(COLON) Complex Numbers

19Lesson 5.1: Introduction To Complex Numbers And The Argand Diagram20Lesson 5.2: Modulus, Argument And The Polar Form21Lesson 5.3: The Exponential Form And Euler's Relation22Lesson 5.4: De Moivre's Theorem And The Roots Of Unity23Lesson 5.5: Loci And Regions In The Complex Plane

6. Topic 6(COLON) Advanced Calculus

24Lesson 6.1: Trigonometric Identities And Equations25Lesson 6.2: Differentiation Review And Standard Derivatives26Lesson 6.3: Implicit And Parametric Differentiation27Lesson 6.4: Inverse Trigonometric And Hyperbolic Functions28Lesson 6.5: Integration Techniques: Substitution And By Parts29Lesson 6.6: Integration Using Partial Fractions And Trigonometric/hyperbolic Substitution30Lesson 6.7: Applications Of Integration

7. Topic 7(COLON) Vectors and Coordinate Geometry

31Lesson 7.1: Vectors In Two And Three Dimensions32Lesson 7.2: The Scalar . Product33Lesson 7.3: The Vector (cross) Product And The Scalar Triple Product34Lesson 7.4: Lines And Planes In Three Dimensions35Lesson 7.5: Conic Sections36Lesson 7.6: Polar Coordinates

8. Topic 8(COLON) Differential Equations

37Lesson 8.1: First-order Separable Differential Equations38Lesson 8.3: Second-order Linear Equations: Homogeneous39Lesson 8.4: Second-order Equations: Particular Integrals And Applications40Lesson 8.5: Coupled And Substitution-reducible Differential Equations

9. Topic 9(COLON) Mathematical Modelling and Numerical Methods

41Lesson 9.1: The Mathematical Modelling Cycle42Lesson 9.2: Numerical Solution Of Equations43Lesson 9.3: Numerical Integration44Lesson 9.4: Numerical Solution Of Differential Equations

10. Topic 10(COLON) Multivariable and Statistical Mathematics

45Lesson 10.1: Functions Of Several Variables And Partial Differentiation46Lesson 10.2: Stationary Points And Constrained Optimisation47Lesson 10.3: Probability And Discrete Distributions48Lesson 10.4: The Normal Distribution And Data Analysis

11. Topic 11(COLON) Academic English for Mathematics (EAP and Study Skills)

49Lesson 11.1: Academic Writing And Mathematical Communication50Lesson 11.2: Referencing, Citation And Academic Integrity51Lesson 11.3: Critical Reading Of Mathematical And Technical Sources52Lesson 11.4: Seminar And Discussion Skills53Lesson 11.5: Academic Presentation Skills54Lesson 11.6: The Independent Research / Modelling Project
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