Mathematics I

What you'll learn

The key areas this subject covers, mapped to the official curriculum.

• Sets, functions and limits
• Rules of differentiation
• Techniques of integration
• Analytical geometry
• Applications of calculus

Course units

The structured path through this subject.

1. 1

   Function of One Variable

   Sets, the real number system and the language of functions.

   4 topics · 4 lessons available

2. 2

   Limits and Continuity

   The limit concept, techniques of evaluating limits and continuity.

   5 topics · 5 lessons available

3. 3

   Derivatives

   Differentiation rules for all the elementary functions and implicit differentiation.

   5 topics · 5 lessons available

4. 4

   Applications of Derivatives

   Tangents, optimization, curve shape and the limit-based tools built on derivatives.

   4 topics · 4 lessons available

5. 5

   Antiderivatives

   Reverse differentiation and the core techniques of integration.

   4 topics · 4 lessons available

6. 6

   Applications of Antiderivatives

   Using integrals to compute areas, volumes, averages and work.

   4 topics · 4 lessons available

7. 7

   Ordinary Differential Equations

   First-order ordinary differential equations and the methods that solve them.

   4 topics · 4 lessons available

8. 8

   Infinite Sequence and Series

   Convergence of sequences and series, tests, and power series representation.

   4 topics · 4 lessons available

9. 9

   Plane and Space Vectors

   Vectors, their products, and the equations of lines and planes in space.

   4 topics · 4 lessons available

10. 10

    Partial Derivatives and Multiple Integrals

    Calculus in two and three dimensions: partial derivatives, chain rules and iterated integrals.

    4 topics · 4 lessons available