This course covers a comprehensive introduction to Calculus 1, including topics such as limits, derivatives, integrals, and their applications. Students will learn skills such as finding limits, differentiating functions, integrating functions, and solving optimization problems. The teaching method involves lecture-style videos. This course is intended for learners interested in gaining a strong foundation in calculus.
Overview
Syllabus
Calculus 1 Lecture 0.1: Lines, Angle of Inclination, and the Distance Formula.
Calculus 1 Lecture 0.2: Introduction to Functions..
Calculus 1 Lecture 0.3: Review of Trigonometry and Graphing Trigonometric Functions.
Calculus 1 Lecture 0.4: Combining and Composition of Functions.
Calculus 1 Lecture 1.1: An Introduction to Limits.
Calculus 1 Lecture 1.2: Properties of Limits. Techniques of Limit Computation.
Calculus 1 Lecture 1.4: Continuity of Functions.
Calculus 1 Lecture 1.5: Slope of a Curve, Velocity, and Rates of Change.
Calculus 1 Lecture 2.1: Introduction to the Derivative of a Function.
Calculus 1 Lecture 2.2: Techniques of Differentiation (Finding Derivatives of Functions Easily).
Calculus 1 Lecture 2.3: The Product and Quotient Rules for Derivatives of Functions.
Calculus 1 Lecture 2.4: Applications of the Derivative.
Calculus 1 Lecture 2.5: Finding Derivatives of Trigonometric Functions.
Calculus 1 Lecture 2.6: Discussion of the Chain Rule for Derivatives of Functions.
Calculus 1 Lecture 2.7: Implicit Differentiation.
Calculus 1 Lecture 2.8: Related Rates.
Calculus 1 Lecture 3.1: Increasing/Decreasing and Concavity of Functions.
Calculus 1 Lecture 3.2: A BRIEF Discussion of Rolle's Theorem and Mean-Value Theorem..
Calculus 1 Lecture 3.3: The First Derivative Test for Increasing and Decreasing.
Calculus 1 Lecture 3.4: The Second Derivative Test for Concavity of Functions.
Calculus 1 Lecture 3.5: Limits of Functions at Infinity.
Calculus 1 Lecture 3.6: How to Sketch Graphs of Functions.
Calculus 1 Lecture 3.7: Optimization; Max/Min Application Problems.
Calculus 1 Lecture 4.1: An Introduction to the Indefinite Integral.
Calculus 1 Lecture 4.2: Integration by Substitution.
Calculus 1 Lecture 4.3: Area Under a Curve, Limit Approach, Riemann Sums.
Calculus 1 Lecture 4.4: The Evaluation of Definite Integrals.
Calculus 1 Lecture 4.5: The Fundamental Theorem of Calculus.
Calculus 1 Lecture 5.1: Finding Area Between Two Curves.
Calculus 1 Lecture 5.2: Volume of Solids By Disks and Washers Method.
Calculus 1 Lecture 5.3: Volume of Solids By Cylindrical Shells Method.
Calculus 1 Lecture 5.4: Finding the Length of a Curve on a Plane.
Taught by
Professor Leonard
