SEMESTER 1 · MA 101 · Calculus I
Mathematics
Read the lessons in order. Each lesson explains the idea, shows it in a diagram, gives the formulas with their conditions, and works through examples step by step.
Lessons
- 01
Functions you need for calculus
The function language that every calculus lesson uses: domains and ranges, piecewise rules, transformations, composition, inverses, exponentials and logarithms, and trigonometric functions in radians.
- 02
Limits
A limit describes the value a function approaches near a point, not the value at the point.
- 03
Continuity
A function is continuous at a point when its limit there exists and equals its value: no holes, jumps or breaks.
- 04
Derivative as a rate
The derivative is the instantaneous rate of change: the limit of average rates, and the slope of the tangent line.
- 05
Differentiation rules
Rules that give derivatives quickly and reliably: power, sum, product, quotient and chain rules, with the derivatives of trigonometric, exponential and logarithmic functions.
- 07
Linear approximation
Near a point, a differentiable function is almost a straight line: its tangent line gives quick estimates and error sizes.
- 08
Rolle and Mean Value Theorems
If a smooth function goes from one value to another, somewhere its instantaneous rate equals its average rate.
- 09
Extrema and curve shape
The first derivative shows where a graph rises and falls; the second shows how it bends. Together they locate maxima, minima and inflection points.
- 10
Optimization
Turn a “best design” question into a function of one variable on an interval, then use derivatives to find and justify the optimum.