Calculus 1 - Full College Course

Basic math review and then more difficult concepts (0:00:00) [Corequisite] Rational Expressions (0:09:40) [Corequisite] Difference Quotient (0:18:20) Graphs and Limits (0:25:51) When Limits Fail to Exist (0:31:28) Limit Laws (0:37:07) The Squeeze Theorem (0:42:55) Limits using Algebraic Tricks (0:56:04) When the Limit of the Denominator is 0 (1:08:40) [Corequisite] Lines: Graphs and Equations (1:17:09) [Corequisite] Rational Functions and Graphs (1:30:35) Limits at Infinity and Graphs (1:37:31) Limits at Infinity and Algebraic Tricks (1:45:34) Continuity at a Point (1:53:21) Continuity on Intervals (1:59:43) Intermediate Value Theorem (2:03:37) [Corequisite] Right Angle Trigonometry (2:11:13) [Corequisite] Sine and Cosine of Special Angles (2:19:16) [Corequisite] Unit Circle Definition of Sine and Cosine (2:24:46) [Corequisite] Properties of Trig Functions (2:35:25) [Corequisite] Graphs of Sine and Cosine (2:41:57) [Corequisite] Graphs of Sinusoidal Functions (2:52:10) [Corequisite] Graphs of Tan, Sec, Cot, Csc (3:01:03) [Corequisite] Solving Basic Trig Equations (3:08:14) Derivatives and Tangent Lines (3:22:55) Computing Derivatives from the Definition (3:34:02) Interpreting Derivatives (3:42:33) Derivatives as Functions and Graphs of Derivatives (3:56:25) Proof that Differentiable Functions are Continuous (4:01:09) Power Rule and Other Rules for Derivatives (4:07:42) [Corequisite] Trig Identities (4:15:14) [Corequisite] Pythagorean Identities (4:20:35) [Corequisite] Angle Sum and Difference Formulas (4:28:31) [Corequisite] Double Angle Formulas (4:36:01) Higher Order Derivatives and Notation (4:39:22) Derivative of e^x (4:46:52) Proof of the Power Rule and Other Derivative Rules (4:56:31) Product Rule and Quotient Rule (5:02:09) Proof of Product Rule and Quotient Rule (5:10:40) Special Trigonometric Limits (5:17:31) [Corequisite] Composition of Functions (5:29:54) [Corequisite] Solving Rational Equations (5:40:02) Derivatives of Trig Functions (5:46:23) Proof of Trigonometric Limits and Derivatives (5:54:38) Rectilinear Motion (6:11:41) Marginal Cost (6:16:51) [Corequisite] Logarithms: Introduction (6:25:32) [Corequisite] Log Functions and Their Graphs (6:36:17) [Corequisite] Combining Logs and Exponents (6:40:55) [Corequisite] Log Rules (6:49:27) The Chain Rule (6:58:44) More Chain Rule Examples and Justification (7:07:43) Justification of the Chain Rule (7:10:00) Implicit Differentiation (7:20:28) Derivatives of Exponential Functions (7:25:38) Derivatives of Log Functions (7:29:38) Logarithmic Differentiation (7:37:08) [Corequisite] Inverse Functions (7:51:22) Inverse Trig Functions (8:00:56) Derivatives of Inverse Trigonometric Functions (8:12:11) Related Rates - Distances (8:17:55) Related Rates - Volume and Flow (8:22:21) Related Rates - Angle and Rotation (8:28:20) [Corequisite] Solving Right Triangles (8:34:54) Maximums and Minimums (8:46:18) First Derivative Test and Second Derivative Test (8:51:37) Extreme Value Examples (9:01:33) Mean Value Theorem (9:09:09) Proof of Mean Value Theorem (0:14:59) [Corequisite] Solving Right Triangles (9:25:20) Derivatives and the Shape of the Graph (9:33:31) Linear Approximation (9:48:28) The Differential (9:59:11) L'Hospital's Rule (10:06:27) L'Hospital's Rule on Other Indeterminate Forms (10:16:13) Newtons Method (10:27:45) Antiderivatives (10:33:24) Finding Antiderivatives Using Initial Conditions (10:41:59) Any Two Antiderivatives Differ by a Constant (10:45:19) Summation Notation (10:49:12) Approximating Area (11:04:22) The Fundamental Theorem of Calculus, Part 1 (11:15:02) The Fundamental Theorem of Calculus, Part 2 (11:22:17) Proof of the Fundamental Theorem of Calculus (11:29:18) The Substitution Method (11:38:07) Why U-Substitution Works (11:40:23) Average Value of a Function (11:47:57) Proof of the Mean Value Theorem for Integrals