Lecture notes

This page contains a wide variety of lecture notes that have been provided by BMT for those clients or students who are interested in learning the following list of classes or courses in Mathematical Sciences. To have access to these lecture notes, simply click on your favorite classes or courses* and follow the displayed instructions**.

* All Lecture Notes related to classes or courses are password protected. The passwords will only be revealed to registered students.

** Registered students may contact us and request other sample lecture notes, if they are not displayed in sections below.

Grade 9 - 12 Math, All Versions.
Grade 11 - 12 Data Management.
Calculus, All Versions at All Levels
Engineering Mathematics
Linear Algebra, All Versions at All Levels
Ordinary Differential Equations
Mathematical Analysis, All Versions
Elementary Numerical Analysis
Introduction to Complex Variables
Applied Complex Variables for Scientists & Engineers
Complex Analysis
Partial Differential Equations
Elementary Probability and its Applications
Mathematical Modelling
General Topology (Topology I)
Algebraic Topology (Topology II)
Elementary Functional Analysis
Fourier Analysis and its Applications
Real Analysis
Real & Complex Analysis
Measure Theory
Functional Analysis
Measure and Integration
Operator Theory
Commutative Banach Algebras
Positive Operators

Grade 9-12 Math: Lecture Notes

Grade 9 Math: Unit 1 (Square Roots & Surface Area).
Grade 9 Math: Unit 2 (Power & Exponent Rules).
Grade 9 Math: Unit 3 (Rational Numbers).
Grade 10 Math: Chapter 1 (Algebraic Expressions).
Grade 10 Math: Lecture Note #1 (Laws of Exponents).
Grade 10 Math: Chapter 2 (Analytic Geometry).
Grade 11 Math: Unit 1 (Relations & functions).
Grade 11 Math: Unit 2 (Polynomials).
Grade 11 Math: Unit 3 (Fundamentals of Trigonometry).
Grade 11-12 Math: Lecture Note A (Pascal Triangles).
Grade 12 Math: Chapter 1 (Polynomial Functions).
Grade 12 Math: Chapter 2 (Rational Functions).
Grade 12 Math: Chapter 3 (Exponential & Logarithm Functions).
Grade 11-12 Math: Lecture Note #2 (Trigonometric Functions).

Grade 11-12 Data Management: Lecture Notes

Data Management: Lecture Note #1 (Counting Techniques).
Data Management: Lecture Note #2 (Organization of Data for Analysis).
Data Management: Lecture Note #3 (Methods of Collecting Data).
Data Management: Lecture Note #4 (Univariate Data Analysis).
Data Management: Introduction (Analysis tools and Analysis Mechanics).
Data Management: Principles of Data Management.
Tools for Data Management: Unit 0 (Basic Concepts in Statistics).
Tools for Data Management: Unit 1 (Graphical Displays of Data).
Tools for Data Management: Unit 2 (Basic Probability).
Tools for Data Management: Unit 3 (Bayes' Theorem & Examples).
Tools for Data Management: Unit 4 (Binomial Distribution).
Tools for Data Management: Unit 5 (Special Random Variables).

Calculus Lecture Notes; All Versions

Pre-Calculus: Chapter 1 (Numbers and Functions).
Pre-Calculus: Chapter2 (Limits and Continuity of Functions).
Calculus I: Brief Lecture Note.
Calculus I: Lecture Note #1 (Limits & Continuity).
Calculus II: Lecture Note #1 (Techniques of Integration).
Calculus II: Lecture Note #2 (Improper Integrals).
Calculus III: Lecture Note #1 (3D Analytic Geometry).
Calculus for Sciences: Chapter 1 (Functions, Graphs, and Limits)
Vector Calculus: Lecture Note #1 (Curves).
Vector Calculus: Lecture Note #2 (Surfaces).
Advanced Calculus: Lecture Note #1 (A Brief Review).
Advanced Calculus: Part I (Review, Cardinality, Induction & Real Numbers).
Advanced Calculus: Part II (Sequences & Series).
Applied Calculus: Lecture Note #1 (Applications of Derivative).
Applied Calculus: Lecture note #2 (Application of Integration).

Engineering Mathematics Lecture Notes

Engineering Mathematics: Lecture Note A (Fourier Series).
Engineering Mathematics: Lecture Note B (Fourier Integrals & Fourier transform).
Engineering Mathematics: Lecture Note C (Bessel's Functions and Their Applications in Solving PDEs)
Engineering Mathematics: Lecture Note D (Legendre Polynomials and Their Applications).
Engineering Mathematics: Lecture Note E (Sturm-Liouville Problems).
Engineering Mathematics: Lecture Note #1 (PDE - Heat in 1D - Separation of Variables).
Engineering Mathematics: Lecture Note #2 (PDE - Wave in 1D - D'Alembert Method)).
Engineering Mathematics: Lecture Note #3 (PDE - Wave in 1D Space - Separation of Variable).
Engineering Mathematics: Lecture Note #4 (PDE - Dirichlet's Problem).
Engineering Mathematics: Lecture Note #5 (Fourier Transform solution of PDEs In Infinite Domain).
Engineering Mathematics: Lecture Note #6 (Solution of PDEs in Polar, Cylindrical & Spherical Coordinates).
Engineering Mathematics: Lecture Note #7 (The Complex Plane).
Engineering Mathematics: Lecture Note #8 (Analytic Functions).
Engineering Mathematics: Lecture Note #9 (Elementary Complex Functions).
Engineering Mathematics: Lecture Note #10 (Complex Line Integrals & Integration).
Engineering Mathematics: Lecture Note #11 (Taylor & Laurent Series).
Engineering Mathematics: Lecture Note #12 (Residue Theorem & Its Applications).

Linear Algebra Lecture Notes: All Versions

Elementary Linear Algebra: Lecture Note #1 (Vectors and Matrices).
Elementary Linear Algebra: Lecture Note #2 (Systems of Linear Equations).
Elementary Linear Algebra: Lecture Note #3 (Determinant & Its Applications).
Elementary Linear Algebra: Lecture Note #4 (Vector Spaces & Their Applications).
Linear Algebra: Lecture Note #1 ( Linear Systems & Matrices).
Linear Algebra: Lecture Note #2 (Vector Spaces).
Linear Algebra: Lecture Note #3 (Linear Transformations).
Linear Algebra: Lecture Note #4 (Polynomials).
Advanced Linear Algebra: Lecture Note A (Fields and Matrix Algebra).
Advanced Linear Algebra: Lecture Note #1 (Linear Spaces and Transformations).
Advanced Linear Algebra: Lecture Note #2 (Vector Spaces with more Detailed Description).
Advanced Linear Algebra: Lecture Note #3 (The Jordan Canonical Form).
Applied Linear Algebra: Lecture Note #1 (Linear Algebraic Systems).
Applied Linear Algebra: Lecture Note #2 (Vector Spaces & Bases).
Applied Linear Algebra: Lecture Note #3 (Inner Products and Norms).

Ordinary Differential Equations

Ordinary Differential Equations: Lecture Note A (Solvable ODEs).
Ordinary Differential Equations: Lecture Note #1 (First Order Linear Differential Equations).
Ordinary Differential Equations: Lecture Note #2 (Exact & Separable Differential Equations).
Ordinary Differential Equations: Lecture Note #3 (Second Order Linear Differential Equations).
Ordinary Differential Equations: Lecture Note #4 (Solving 2nd Order Linear ODEs).
Ordinary Differential Equations: Lecture Note #5 (Method of Variation of Parameters).
Ordinary Differential Equations: Lecture Note #6 (Method of Undetermined Parameters).
Ordinary Differential Equations: Lecture Note #7 (Method of Series Solutions).
Ordinary Differential Equations: Lecture Note #8 (Laplace Transform).
Ordinary Differential Equations: Lecture Note #9 (Method of Laplace Transform).
Ordinary Differential Equations: Lecture Note #10 (Bessel's Equations & Functions).
Ordinary Differential Equations: Lecture Note #11 (Systems of Ordinary Differential Equations).
Ordinary Differential Equations: Lecture Note #12 (Legendre's Equations & Functions).

Mathematical Analysis Lecture Notes: All Versions

Fundamentals of Mathematical Analysis: Lecture Note #1 (Elements of Logic and Set Theory).

Fundamentals of Mathematical Analysis: Lecture Note #2 (Numbers).

Fundamentals of Mathematical Analysis: Lecture Note #3 (Sequences and Limits).

Introduction to Mathematical Analysis: Lecture Note #1 (The Real Number System).

Introduction to Mathematical Analysis: Lecture Note #2 (Continuous Functions).

Introduction to Mathematical Analysis: Lecture Note #3 (Real and Complex Sequences).

Mathematical Analysis I: Lecture Note #1 (The Real and Complex Number Systems).

Mathematical Analysis I: Lecture Note #2 (Basic Topology).

Mathematical Analysis I: Lecture Note #3 (Numerical sequences and Series).

Mathematical Analysis II: Lecture Note #1 (Sequences and Series of Functions).