Learn the fundamental concepts of differential calculus through this comprehensive 11-hour video course covering limits, derivatives, and their applications. Master the introduction to limits including piece-wise functions, discontinuities, and limit laws while developing skills in finding limits algebraically through various examples and challenging problems. Explore continuity concepts, continuity laws, and the Intermediate Value Theorem, then advance to limits at infinity, horizontal asymptotes, and the Squeeze Theorem with practical applications. Dive into derivatives starting with tangent lines, rates of change, and the definition of derivatives, progressing through notation and higher derivatives. Study essential differentiation rules including the power rule, product rule, quotient rule, and chain rule with extensive examples and practice problems. Examine trigonometric derivatives, implicit differentiation, inverse trigonometric derivatives, and logarithmic differentiation techniques. Apply derivative concepts to solve related rates problems, find maximum and minimum values, and understand the Extreme Value Theorem and Mean Value Theorem. Develop curve sketching skills using the first and second derivative tests, tackle optimization problems, and explore Newton's Method and L'Hospital's Rule. Conclude with parametric equations, polar coordinates, polar curves, and an introduction to antiderivatives, with additional practice through university-level quiz problems from UBC and McGill.

Syllabus

INTRODUCTION to LIMITS - CALCULUS
[Calculus] Piece-wise Functions, Discontinuities, and Limits.
LIMIT LAWS - CALCULUS
FINDING LIMITS ALGEBRAICALLY - CALCULUS
[Calculus] Limit Examples
[Calculus] Challenging Limits Examples
[Calculus] Precise Definition of a Limit
CONTINUITY - CALCULUS
EXERCISE in CONTINUITY - CALCULUS
EXERCISES in CONTINUITY - CALCULUS
[Calculus] Continuity Laws
[Calculus] Intermediate Value Theorem
[Calculus] Limits at Infinity, Horizontal Asymptotes
[Calculus] Limits at Infinity Examples
[Calculus] Squeeze Theorem
[Calculus] Squeeze Theorem Examples
[Calculus] Limit Practice #1
[Calculus] Tangent Lines
[Calculus] Derivates and Rate of Change
[Calculus] Definition of the Derivative Examples
[Calculus] Notation and Higher Derivatives
[Calculus] Limit Practice 2
[Calculus] Basic Differentiation Rules || Lecture 16
[Calculus] Power Rule Examples
[Calculus] Equations of Tangent Lines Examples
[Calculus] Challenging Equations of Tangent Lines Examples
[Calculus] Product Rule || Lecture 17
[Calculus] Quotient Rule || Lecture 18
[Calculus] Product and Quotient Rule Examples
[Calculus] Chain Rule || Lecture 19
[Calculus] Trigonometric Derivatives || Lecture 20
[Calculus] Derivative Practice 1 || Lecture 21
[Calculus] UBC Math 100-180 Midterm 1
[Calculus] Implicit Differentiation || Lecture 22
[Calculus] Inverse Trigonometric Derivatives || Lecture 23
[Calculus] Derivatives of Logarithms || Lecture 24
[Calculus] Logarithmic Differentiation || Lecture 25
[Calculus] Derivative Practice 2 || Lecture 26
[Calculus] Related Rates || Lecture 27
[Calculus] Maximum and Minimums || Lecture 28
[Calculus] Extreme Value Theorem || Lecture 29
[Calculus] Mean Value Theorem || Lecture 30
[Calculus] First Derivative Test || Lecture 31
[Calculus] Second Derivative Test || Lecture 32
[Calculus] Curve Sketching || Lecture 33
[Calculus] Optimization 1 || Lecture 34
[Calculus] Optimization 2 || Lecture 35
[Calculus] Newton's Method || Lecture 36
[Calculus] L'Hospital's Rule || Lecture 37
[Calculus] Parametric Equations || Lecture 38
[Calculus] Polar Coordinates || Lecture 39
[Calculus] Polar Curves || Lecture 40
[Calculus] Antiderivatives || Lecture 41
[Calculus] McGill Math 139 - Quiz 2
[Calculus] McGill Math 139 - Quiz 3
How to use CONTINUITY LAWS - CALCULUS