Embark on a comprehensive journey through Calculus 1 with this extensive video lecture series. Master fundamental concepts from algebra and trigonometry review to advanced calculus topics. Explore limits, derivatives, integrals, and their practical applications. Dive deep into each subject with detailed lectures covering lines, functions, trigonometry, continuity, slopes, rates of change, differentiation techniques, implicit differentiation, related rates, function behavior, theorems, graphing, optimization, integration methods, area under curves, volumes of solids, and curve lengths. Gain a solid foundation in calculus through clear explanations and numerous examples provided throughout the course.
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
