Topic 1 Overview of Continuity Continuity: Radical Functions Continuity: Rational Functions Continuity: Trig Functions Continuity: Logarithms Continuity: Piecewise Functions Introduction to Limits Properties of Limits Limits on a Graph Computing Limits Algebraically -Finite Values One Sided Limits Trigonometric Limits Limits to Infinity – Rational Functions Limits to Infinity – Trig and Unique Examples Instantaneous Rates of Change The Limit Definition of the Derivative Topic 2 Basic Rules of Differentiation The Power Rule (Proof) Derivatives of Sine and Cosine (Proof) Derivatives of Tan, Cot, Csc, Sec Derivatives of Logarithms (Proof) Derivatives of Exponentials (Proof) Differentiability of a Function The Quotient Rule (Proof) Derivatives of Inverse Sine and Cosine (Proof) Derivatives of Inverse Secant and Cosecant (Proof) Derivatives of Inverse Tangent and Cotangent (Proof) Recap of Inverse Trig Derivatives Mastering the Chain Rule Implicit Differentiation Topic 3 Rates of Change Maxima and Minima Concavity Points of Inflection Identifying Concavity Easily Relationships Between f, f’, and f” Anaylzing Functions Algebraically Motion: Position, Velocity, and Acceleration Related Rates Optimization Mean Value Theorem and Rolle’s Theorem L’Hopital’s Rule Linearization Differentials and Estimated Error Topic 4 Introduction to the Definite Integral Riemann Sums Important Notes for Riemann Sums Exacting Areas with Riemann Sums Trapezoidal Sums The Antiderivative Basic Rules of Integration Fundamental Theorem of Calculus & Properties of Definite Integrals Net Area vs Total Area Integration by Substitution (Indefinite) Integration by Substitution (Definite) Integration by Substitution (Logarithms and Inverse Trig) Functions Defined as Integrals and the \[2^{nd}\] Fundamental Theorem of Calculus Topic 5 Area Between Curves Mean Value Theorem and Rolle’s Theorem Rectilinear Motion Revisited Volumes Based on Known Cross Sections Volumes – The Disk Method Volumes – The Washer Method Volumes – The Shell Method Topic 6 Differential Equations Slope Fields Overview of Growth and Decay Models Study Guide Flash Cards ← Previous Lesson Next Lesson → Topic 1 Overview of Continuity Continuity: Radical Functions Continuity: Rational Functions Continuity: Trig Functions Continuity: Logarithms Continuity: Piecewise Functions Introduction to Limits Properties of Limits Limits on a Graph Computing Limits Algebraically -Finite Values One Sided Limits Trigonometric Limits Limits to Infinity – Rational Functions Limits to Infinity – Trig and Unique Examples Instantaneous Rates of Change The Limit Definition of the Derivative Topic 2 Basic Rules of Differentiation The Power Rule (Proof) Derivatives of Sine and Cosine (Proof) Derivatives of Tan, Cot, Csc, Sec Derivatives of Logarithms (Proof) Derivatives of Exponentials (Proof) Differentiability of a Function The Quotient Rule (Proof) Derivatives of Inverse Sine and Cosine (Proof) Derivatives of Inverse Secant and Cosecant (Proof) Derivatives of Inverse Tangent and Cotangent (Proof) Recap of Inverse Trig Derivatives Mastering the Chain Rule Implicit Differentiation Topic 3 Rates of Change Maxima and Minima Concavity Points of Inflection Identifying Concavity Easily Relationships Between f, f’, and f” Anaylzing Functions Algebraically Motion: Position, Velocity, and Acceleration Related Rates Optimization Mean Value Theorem and Rolle’s Theorem L’Hopital’s Rule Linearization Differentials and Estimated Error Topic 4 Introduction to the Definite Integral Riemann Sums Important Notes for Riemann Sums Exacting Areas with Riemann Sums Trapezoidal Sums The Antiderivative Basic Rules of Integration Fundamental Theorem of Calculus & Properties of Definite Integrals Net Area vs Total Area Integration by Substitution (Indefinite) Integration by Substitution (Definite) Integration by Substitution (Logarithms and Inverse Trig) Functions Defined as Integrals and the \[2^{nd}\] Fundamental Theorem of Calculus Topic 5 Area Between Curves Mean Value Theorem and Rolle’s Theorem Rectilinear Motion Revisited Volumes Based on Known Cross Sections Volumes – The Disk Method Volumes – The Washer Method Volumes – The Shell Method Topic 6 Differential Equations Slope Fields Overview of Growth and Decay Models Study Guide Flash Cards Share this:Click to share on Twitter (Opens in new window)Click to share on Facebook (Opens in new window)Click to share on Google+ (Opens in new window) More Videos Submit a Comment Cancel replyYou must be logged in to post a comment.