Title: HELM Workbooks 2023-2024

Section 1
  Announcements
HELM 1: Basic Algebra
  1_1 Mathematical Notation and Symbols
  1_2 Indices
  1_3 Simplification and Factorisation
  1_4 Arithmetic of Algebraic Fractions
  1_5 Formulae and Transposition
HELM 2: Basic Functions
  2_1 Basic Concepts of Functions
  2.1 Basic Concepts of Functions (copy)
  2_2 Graphs of Functions and Parametric Form
  2_3 One-to-One and Inverse Functions
  2_4 Characterising Functions
  2_5 The Straight Line
  2_7 Some Common Functions
HELM 3: Equations, Inequalities and Partial Fractions
  3_1 Solving Linear Equations
  3_2 Solving Quadratic Equations
  3_3 Solving Polynomial Equations
  3_4 Solving Simultaneus Linear Equations
  3_5 Solving Inequalities
  3_6 Partial Fractions
HELM 4: Trigonometry
  4_2 Trigonometric Functions
  4_3 Trigonometric Identities
  4_5 Applications of Trigonometry to Waves
HELM 5: Functions and Modeling
  5_2 Quadratic Functions and Modelling
  5_3 Oscillating Functions and Modelling
  5_4 Inverse Square Law Modelling
HELM 6: Exponential and Logarithmic Functions
  6_1 The Exponential Function
  6_2 The Hyperbolic Functions
  6_3 Logarithms
  6_4 The Logarithmic Function
HELM 7: Matrices
  7_1 Introduction to Matrices
  7_2 Matrix Multiplication
  7_3 Determinants
  7_4 The Inverse of a Matrix
HELM 8: Matrix Solution of Equations
  8_1 Solution by Cramer's Rule
  8_2 Solution by Inverse Matrix Method
  8_3 Solution by Gauss Elimination
HELM 9: Vectors
  9_1 Basic concepts of vectors
  9_2 Cartesian Components of Vectors
  9_3 The Scalar Product
  9_4 The Vector Product
  9_5 Lines and Planes
HELM 10: Complex Numbers
  10_1 Complex Arithmetic
  10_2 The Argand Diagram and Polar form
  10_3 The Exponential Form of a Complex Number
  10_4 De Moivre’s Theorem
HELM 11: Differentiation
  11_1 Introducing Differentiation
  11_2 Using a Table of Derivatives
  11_3 Higher Derivatives
  11_4 Differentiating Products and Quotients
  11_5 The Chain Rule
  11_6 Parametric Differentiation
  11_7 Implicit Differentiation
HELM 12: Applications of Differentiation
  12_1 Tangents and Normals
  12_2 Maxima and Minima
  12_3 The Newton–Raphson Method
  12_5 Differentiation of Vectors
HELM 13: Integration
  13_1 Basic Concepts of Integration
  13_2 Definite Integrals
  13_3 The Area Bounded by a Curve
  13_4 Integration by Parts
  13_5 Integration by Substitution and Using Partial Fractions
  13_6 Integration of Trigonometric Functions
HELM 14: Applications of Integration 1
  14_1 Integration as the Limit of a Sum
  14_2 The Mean Value and the Root-Mean-Square Value
  14_3 Volumes of Revolution
  14_4 Lengths of Curves and Surfaces of Revolution
HELM 15: Applications of Integration 2
  15_2 Calculating Centres of Mass
HELM 16: Sequences and Series
  16_1 Infinite Sequences and Finite Series
  16_2 Infinite Series and convergence tests
  16_3 The Binomial Series
  16_4 Power Series
  16_5 Maclaurin and Taylor Series
HELM 18: Functions of Several Variables
  18_1 Functions of Several Variables
  18_2 Partial Derivatives (origal HELM)
  18_3 Stationary Points
  18_3 Stationary Points new
  18_4 Errors and Percentage Change
HELM 19: Differential Equations
  19_1 Modelling with Differential Equations
  19_2 First Order Differential Equations
  19_3 Second Order Differential Equations
HELM 22: Eigenvalues and Eigenvectors
  22_1 Basic Concepts of Eigenvalues and Eigenvectors
  22_2 Applications of Eigenvalues and Eigenvectors
  22_3 Repeated Eigenvalues and Symmetric Matrices
HELM 35: Sets and Probability
  35_1 Sets
  35_2 Elementary Probability
  35_3 Addition and Multiplication Laws of Probability
  35_4 Total Probability and Bayes’ Theorem
HELM 36: Descriptive Statistics
  36_1 Describing Data
  Describing Data (Edinburgh)
  36_2 Exploring Data
  Exploring Data (Edinburgh)
HELM 37: Discrete Probability Distributions
  37_1 Discrete Probability Distributions
  37_2 The Binomial Distribution
  37_3 The Poisson Distribution
HELM 38: Continuous Probability Distributions
  38_1 Continuous Probability Distributions
  38_2 The Uniform Distribution
  38_3 The Exponential Distribution
HELM 39: The Normal Distribution
  39_1 The Normal Distribution
HELM 20: Laplace Transforms
  20.1 Casual Functions
  20.2 The Transform and its Inverse
  20.3 Further Laplace Transforms
  20.4 Solving Differential Equations
  20.5 The Convolution Theorem
  20.6 Transfer Functions
HELM 23: Fourier Series
  23.1 Periodic Functions
  23.2 Representing Periodic Functions by Fourier Series
  23.3 Even and Odd Functions
  23.4 Convergence
  23.5 Half-Range Series
  23.6 The Complex form
  23.7 An Application of Fourier Series
HELM 25: Partial Differential Equations
  25.1 Partial Differential Equations
  25.2 Applications of PDEs
  25.3 Solution Using Separation of Variables
  25.4 Solution Using Fourier Series