"Mathematics knows no races or geographic boundaries; for mathematics, the cultural world is one country."   -David Hilbert ·


Below are my handwritten lecture notes on pre and introductory Calculus. Each topic area contains a problem set and a set of lecture notes. The questions in the problem set are worked through in the lecture notes. 


Copyright Notice:  ©Dilshara Hill.    This material is available free to all individuals, on the understanding that it is not to be used for financial gains, and may be downloaded and/or printed for personal use, with or without permission from the author. However, this material may not be kept on any information storage and retrieval system without permission from the author.

Pre-Calculus:

1. Foundational Maths

Problem Set 1

Lecture 1 – Foundational Maths

Lecture 2 – Foundational Maths

Lecture 3 – Foundational Maths

Lecture 4 – Foundational Maths

2. Introduction to Algebra

Problem Set 2

Lecture 1 – Intro to Algebra

Lecture 2 – Intro to Algebra

Lecture 3 – Intro to Algebra

3. Algebra

Problem Set 3

Lecture 1 – Algebra

Lecture 2 – Algebra

Lecture 3 – Algebra

4. Lines

Problem Set 4

Lecture 1 – Lines

Lecture 2 – Lines

Lecture 3 – Lines

5. Quadratics

Problem Set 5

Lecture 1 – Quadratics

Lecture 2 – Quadratics

Lecture 3 – Quadratics

6. Functions

Problem Set 6

Lecture 1 – Functions

Lecture 2 – Functions

Lecture 3 – Functions

7. More on Functions

Problem Set 7

Lecture 1 – More Functions

Lecture 2 – More Functions

Lecture 3 – More Functions

8. Exponentials

Problem Set 8

Lecture 1 – Exponentials

Lecture 2 – Exponentials

Lecture 3 – Exponentials

9. Logarithms

Problem Set 9

Lecture 1 – Logarithms

Lecture 2 – Logarithms

Lecture 3 – Logarithms

10. Logs & Exponentials

Problem Set 10

Lecture 1 – Logs&Exp

Lecture 2 – Logs&Exp

Lecture 3 – Logs&Exp

11. Polynomials

Problem Set 11

Lecture 1 – Polynomials

Lecture 2 – Polynomials

Lecture 3 – Polynomials

Lecture 4 – Polynomials

Lecture 5 – Polynomials

12. Arithmetic & Geometric Progressions

Problem Set 12

Lecture 1 – Progressions

Lecture 2 – Progressions

Lecture 3 – Progressions

13. Inequalities

Problem Set 13

Lecture 1 – Inequalities

Lecture 2 – Inequalities

Lecture 3 – Inequalities
Trigonometry & Introductory Calculus:

14. Introduction to Trigonometry

Problem Set 14

Lecture 1 – Intro to Trig

Lecture 2 – Intro to Trig

Lecture 3 – Intro to Trig

15. Trigonometry

Problem Set 15

Lecture 1 – Trigonometry

Lecture 2 – Trigonometry

Lecture 3 – Trigonometry

16. Introduction to Differentiation

Problem Set 16

Lecture 1 – Intro to Differentiation

Lecture 2 – Intro to Differentiation

Lecture 3 – Intro to Differentiation

17. More Differentiation

Problem Set 17

Lecture 1 – Differentiation

Lecture 2 – Differentiation

Lecture 3 – Differentiation

18. Differentiation & Curve Sketching

Problem Set 18

Lecture 1 – Differentiation & Curve Sketching

Lecture 2 – Differentiation & Curve Sketching

Lecture 3 – Differentiation & Curve Sketching

19. Applications of Differentiation

Problem Set 19

Lecture 1 – Applications of Differentiation

Lecture 2 – Applications of Differentiation

20. Introduction to Integration

Problem Set 20

Lecture 1 – Intro to Integration

Lecture 2 – Intro to Integration

Lecture 3 – Intro to Integration

21. More Integration

Problem Set 21

Lecture 1 – Integration

Lecture 2 – Integration

Lecture 3 – Integration

22. Areas & Integration

Problem Set 22

Lecture 1 – Areas & Integration

Lecture 2 – Areas & Integration

Lecture 3 – Areas & Integration

23. Integration Techniques

Problem Set 23

Lecture 1 – Integration Techniques

Lecture 2 – Integration Techniques

Lecture 3 – Integration Techniques