Laplace Transforms & Applications: Engineering Mathematics Mastery
Master Laplace transforms step-by-step without textbook overwhelm: 7 core transform rules, operational theorems, Heaviside cover-up partial fractions, completing the square, and solving ODEs.
- 4
- Chapters
- 16
- Topics
- 112
- Lessons
- 800
- Total XP
About this course
A beginner-friendly, calculation-first university engineering mathematics course on Laplace Transforms (based on K.A. Stroud & Dexter J. Booth, Programme 2). Every concept is broken down into plain-English rules and solved line-by-line: standard transforms, linear combinations, First Shift Theorem, multiplying and dividing by t, partial fractions (cover-up rule, repeated factors, quadratic factors, completing the square), and solving 1st-order, 2nd-order, and simultaneous differential equations.
What you'll learn
- Calculate Laplace transforms of constants, exponentials, powers of t, sines, cosines, and hyperbolics using 7 simple rules
- Combine linear sums of transforms over a single common denominator without skipping algebra steps
- Apply the 3 Operational Theorems: First Shift Theorem, Multiplying by t, and Dividing by t
- Invert s-domain fractions using Heaviside cover-up, [s^2] and [CT] coefficient equating, and completing the square
Prerequisites
- Basic differential and integral calculus (derivatives, integration by parts)
- Basic algebraic manipulation and quadratic equations
Course outline
Chapter 1
Chapter 1: Standard Laplace Transforms & Linear Combinations
4 topics
Chapter 1
Chapter 1: Standard Laplace Transforms & Linear Combinations
Learn how Laplace transforms turn time functions into simple algebraic s-fractions using 7 core rules, step-by-step worked examples, and single-fraction combinations.
- 1.1 The Laplace Shortcut: Transforming Constants & Exponentials (a and e^{at})
- 1.2 Transforming Powers of t: The Factorial Rule (n! / s^{n+1})