Video Supplement for Math 1b


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5.1 Areas Areas and Distances Section 5.1 Estimating Area with Rectangles Part 1 of 2 Definition of Area of Riemann Sum Limit of Sums Part 2 of 2, Estimating Area with Riemann Sums Finite Rectangles Area Under a Curve, Limit Approach, Riemann Sums Midpoint, Left & Right Endpoints, Area, Definite Integral, Sigma Notation, Calculus
5.2 The Definite Integral The Definite Integral Riemann sums and integrals, Introduction to definite integrals, Definite integrals (part II), Definite integrals (part III), Definite Integrals (part IV), Definite Integrals (part V) The Definite Integral: Understanding the Definition, Calculating a Definite Integral Using Riemann Sums - Part 1, Calculating a Definite Integral Using Riemann Sums - Part 2 Definite Integrals Section 5.2 Estimating Area with Rectangles & Riemann Limit of Sums Definition of Area, Definite Integrals Defined w. Riemann Limit of Sums Example, Definite Integrals Common Geometric Area Area Under a Curve, Limit Approach, Riemann Sums Definite Integral, Properties of Definite Integrals Examples - Basic Overview, Calculus
5.3 The Fundamental Theorem of Calculus and Indefinite Integrals The Fundamental Theorem of Calculus Fundamental Theorem of Calculus The Fundamental Theorem of Calculus Part 1, The Fundamental Theorem of Calculus Part 2 Lecture 19: First fundamental theorem of calculus, Lecture 20: Second fundamental theorem, Lecture 21: Applications to logarithms and geometry Section 5.3 First Fundamental Theorem of Calculus, Definite Integral as a Function of x, Second Fundamental Theorem of Calculus The Fundamental Theorem of Calculus FTC Example 1, FTC Example 2 Fundamental Theorem of Calculus Part 1, Fundamental Thereom of Calculus Explained - Part 1 & 2 Examples, Fundamental Theorem of Calculus Part 2
5.4 The Fundamental Theorem of Calculus and Indefinite Integrals The Indefinite Integral and Net Change Theorem Section 5.4 The Evaluation of Definite Integrals
5.5 The Substitution Rule Substitution Rule Definite Integral with Substitution, U-Substitution, U-substitution example 2, U-substitution Example 3, Another u-substitution example, U-substitution and back substitution, Indefinite Integration (part IV) Integration using U-Substitution, Integration by U-Substitution, Definite Integral, U-substitution - Indefinite Integral, Another 2 examples, U-Substitution - More Complicated Examples Definite Integral by Substitution | MIT 18.01SC Single Variable Calculus, Fall 2010 Section 5.5 Indefinite Integration by U Substitution, Definite Integration with U Substitution Integration by Substitution how to integrate using u substitution How To Integrate Using U-Substitution, U-substitution With Definite Integrals Math 2B. Calculus. Lecture 06. The Substitution Rule., Differential & Integral Calculus, Lec 21, Math 31A, UCLA
6.1 Area Between Curves Introduction to Areas Between Curves, Basic example on finding the area between two curves, Another example on finding the area between two curves, Finding Area Between Curves by Integrating With Respect To y Area between curves Finding Areas Between Curves, Area Between Curves - Integrating with Respect to y Area between curves Section 6.1 Area Between 2 Curves using Vertical and Horizontal Representative Rectangles Finding Area Between Two Curves Area Between Two Curves Math 2B. Calculus. Lecture 07. Areas Between Curves
6.2 Volume Solid of Revolution (part 1), Solid of Revolution (part 2), Solid of Revolution (part 3), Solid of Revolution (part 4), Solid of Revolution (part 5), Solid of Revolution (part 6), Solid of Revolution (part 7), Solid of Revolution (part 8) Volumes of Revolution - Disk/Washers Example 1 Lecture 22 Section 6.2 Volume of Solid of Revolution Disk Method and Washer Method Volume of Solids By Disks and Washers Method Disk & Washer Method Math 2B. Calculus. Lecture 08. Calculating The Volume of Solids.
6.3 Shell method for rotating around horizontal line Longer Version - Volumes using Cylindrical Shells, Volumes of Revolution - Cylindrical Shells Volume of Revolution via Shells | MIT 18.01SC Single Variable Calculus, Fall 2010 Section 6.3 Volume of Solid of Revolution Shell Method 3 Examples Calculus 1 Lecture 5.3: Volume of Solids By Cylindrical Shells Method Shell Example 1, Shell Example 2, Shell Example 3, Shell Example 4 Shell Method - Volume of Revolution
6.4 Work in the case of constant force, Finding work done by springs, Example on finding the work done when stretching a spring, Example on finding the work done to lift a rope, Finding the work done in lifting problems Calculating the Work Required to Drain a Tank, Finding Work using Calculus - The Cable/Rope Problem, Finding Work using Calculus - The Cable/Rope Problem - Part b, Section 6.4 Work Done by a Variable Force Work Example 1, Work Example 2, Work Example 3, Work Example 4, Work Example 5 Work Problems, Work Done By a Variable Force Physics Problems, Force Displacement Graphs
7.1 Integration by Parts Introduction to Integration by Parts, Two examples using integration by parts, Two more examples using integration by parts, Volume application using integration by parts Deriving integration by parts formula, Integration by parts of (e^x)(cos x), Integration by parts twice for antiderivative of (x^2)(e^x), Antiderivative of xcosx using integration by parts Integration by Parts, Integration By Parts - Using IBP's Twice, Integration by Parts - Definite Integral, Integration by Parts - A Loopy Example! Lec 30 | MIT 18.01 Single Variable Calculus, Fall 2007, Finding u and v' When Integrating by Parts | MIT 18.01SC Single Variable Calculus, Fall 2010 Section 7.1 Integration by Parts 6 Examples LIATE, Definite Integration by Parts, Integration by Parts 2 Times 2 Examples Integration by Parts Integration by Parts Integration By Parts, 3- Product Term, Tablular Method Math 2B. Calculus. Lecture 10. Integration by Parts
7.2 Trigonometric Integrals Trig Antiderivative Rules and Key Trig Identities, Integrating products of powers of sines and cosines, Example on integrating products of even powers of sines and cosines, Example on integrating products of powers of tangents and secants, Another example on integrating products of powers of secants and tangents, Example on integrating powers of tangent Trig identities for trig integral Trigonometric Integrals - Part 1 of 6, Trigonometric Integrals - Part 2 of 6, Trigonometric Integrals - Part 3 of 6, Trigonometric Integrals - Part 4 of 6, Trigonometric Integrals - Part 5 of 6, Trigonometric Integrals - Part 6 of 6 Lec 27 | MIT 18.01 Single Variable Calculus, Fall 2007, Trig Integral Practice | MIT 18.01SC Single Variable Calculus, Fall 2010, Trig Integrals and a Volume of Revolution | MIT 18.01SC Single Variable Calculus, Fall 2010 Section 7.2 Trigonometric Integrals Trigonometric Integrals Example 1, Example 2, Example 3, Example 4, Example 5, Example 6 Trigonometric Integrals Math 2B. Calculus. Lecture 11. Trigonometric Integrals
7.3 Trigonometric Substitution Introduction to Trig Substitution, Example using trig sub on an indefinite integral , Example requiring completing the square before using trig substitution, Another example requiring completing the square before using trig substitution, Example using trig sub on a definite integral Integrals: Trig Substitution 1, Integrals: Trig Substitution 2, Integrals: Trig Substitution 3 (long problem), Trig and U substitution together (part 1), Trig and U substitution together (part 2) Trigonometric Substitution - Example 1, Trigonometric Substitution - Example 2, Trigonometric Substitution - Example 3 / Part 1, Trigonometric Substitution - Example 3 / Part 2, Trigonometric Substitution, Ex 4 - Rational Powers, Trigonometric Substitutions - More Examples, Trigonometric Substitution and a Definite Integral , Trigonometric Substitution Example 1 Part 1, Trigonometric Substitution Example 1 Part 2 Lec 28 | MIT 18.01 Single Variable Calculus, Fall 2007 Section 7.3 Trigonometric Substitution 1, Tirognometric Substitution 2 Trigonometric Substitution Example 1, Example 2, Example 3, Example 4, Example 5 Trigonometric Substitution Math 2B. Calculus. Lecture 12. Trigonometric Substitution
7.4 Integration of Rational Functions Partial Fraction Decomposition, Introduction, Forms, Example 1, Example 2, Example 3, Example 4, Example 5, Example 6 Partial fraction expansion to evaluate integral Partial Fraction Decompositions, Integration Using method of Partial Fractions , Integration Using Partial Fractions / Rationalizing Sub MIT Lecture 29 Section 7.4 Partial Fractions 1, Partial Fractions 2, Partial Fractions 3, Integration by Partial Fractions Example 1, Example 2, Example 3, Example 4, Example 5 Integration By Partial Fractions, Partial Fraction Decomposition Math 2B. Calculus. Lecture 13. Integration by Partial Fractions
7.5 Overview of strategy for integration Section 7.5
7.6 Section 7.6 Integration by Tables Integration using Tables
7.7 Approximate Integration Trapezoidal approximation of area under curve, Rectangular and trapezoidal Riemann approximations Simpsons Rule - Approximate Integration, Simpson's Rule - Error Bound, Simpson's Rule - The Derivation, The Trapezoid Rule for Approximating Integrals Using the Trapezoid and Simpson's rules | MIT 18.01SC Single Variable Calculus, Fall 2010, Explanation of Simpson's rule | MIT 18.01SC Single Variable Calculus, Fall 2010 Section 7.7 Trapezoidal Rule Numerical Integration With Trapezoidal and Simpson's Rule Midpoint Rule vs. Trapezoidal Rule, Error Bounds, Trapezoidal Rule Example Trapezoidal Rule, Trapezoidal Rule & Simpson's Rule
7.8 Improper Integrals Introduction to Improper Integrals, Examples of improper integrals with infinite intervals, Evaluating an improper integral of type 1 using multiple integration techniques, Definition of Improper Integrals of Type II and three examples, Example evaluating an improper integral using integration by parts, Introduction to Comparison Theorem for Improper Integrals and an Example, Examples using the Comparison Theorem for Improper Integrals Introduction to improper integrals, Improper integral with two infinite bounds, Divergent improper integral Improper Integral - Basic Idea and Example, Improper Integral - More Complicated Example, Improper Integral - Infinity in Upper and Lower Limits, Improper Integral w/ Infinite Discontinuity in the Middle, Improper Integral with Infinite Discontinuity at Endpoint Improper Integrals | MIT 18.01SC Single Variable Calculus, Fall 2010, Lec 36 | MIT 18.01 Single Variable Calculus, Fall 2007 Section 7.8 Improper Integrals Improper Integrals Improper Integral Example 1, Improper Integral Example 2, Comparison Theorem for Improper Integral, Comparison Theorem Example Improper Integrals Math 2B. Calculus. Lecture 16. Improper Integrals
8.1 Arc Length Introduction to arc length, First example using arc length formula, Another example using arc length formula, Definition of arc length function and an example Non rigorous justification for arc length formula, Arc length integration example, Another arc length integration example Arc Length Formula - Example 1, Arc Length, Arc Length Formula - Example 2 Section 8.1 Arc Length of a Curve ( Smooth Curve ) 5 Examples Finding the Length of a Curve on a Plane Proof, Example Arc Length Problems Math 2B. Calculus. Lecture 17. Arc Length, Review Integration Techniques
8.2 Introduction to Surface Area , Examples on finding the surface area when a curve is rotated about the x-axis, Examples finding surface area when a curve is rotated about the y-axis Finding Surface Area - Part 1, Finding Surface Area - Part 2 Section 8.2 Area of a Surface of Revolution 1, Area of a Surface of Revolution 2, Proof, Example Surface Area
8.3 How to compute hydrostatic force on a dam, Example computing the hydrostatic force on a vertical plate Hydrostatic Force - Complete Example #1, Hydrostatic Force - Basic Idea / Deriving the Formula, Hydrostatic Force - Complete Example #2, Part 1 of 2, Hydrostatic Force - Complete Example #2, Part 2 of 2, Centroid Part 1, Centroid Part 2 Section 8.3 Fluid Pressure and Fluid Force Force Example 1, Force Example 2, Force Example 3, Force Example 4, Force Example 5, Force Example 6, Centroid Proof, Centroid Example Hydrostatic Force Problems, Center of Mass and Centroid Problems, Moment, Center of Mass, and Centroid
8.5 Section 8.5
9.1 Modelling with Differential Equations Modeling population with simple differential equation The Logistic Equation and Models for Population - Example 1, part 1 Section 9.1 Verifying Particular Solutions to Differential Equations
9.2 Section 9.2
9.3 Separable Equations Separable differential equations introduction | First order differential equations Solving Separable First Order Differential Equations - Ex 1, Separable Differential Equation, Example 2 Separable Equations Section 9.3 Intro to Solving Separable Differential Equation, Separable Differential Equations & Growth and Decay Model Solving First Order Differential Equations by Separation of Videos Separable Equation Example, Separable Equation Application Separable First Order Differential Equations
9.4 Section 9.4
9.5 Linear Equations First Order Linear Differential Equations Solutions of First-order Linear Equations Section 9.5 Intro to First-Order Equations, Solving Linear Differential Equations with an Integrating Factor First Order Linear Differential Equation & Integrating Factor First Order Linear Differential Equations
10.1 Introduction to Curves Defined by Parametric Equations, Four examples on sketching parametric curves and eliminating the parameter, Creating parametric equations for a given Cartesian equation Parametric Equations 1, Parametric Equations 2 Parametric Equations - Some basic questions, Parametric Curves - Basic Graphing Parametric equations, arclength, surface area Section 10.1 Introduction to Parametric Equations Parametric Equations Parametric Equations Example Parametric Equations Introduction, Eliminating The Paremeter t, Graphing Plane Curves
10.2 Introduction to the parametric form of the derivative, Finding horizontal and vertical tangents to parametric curves, Finding the area of a region enclosed by a parametric curve, Finding the arc length of a parametric curve, Finding the surface area when a parametric curve is rotated about the x or y axis Derivatives of Parametric Fuctions Parametric equations, arclength, surface area Section 10.2 Calculus of Parametric Equations Arc Length Example Derivatives of Parametric Functions, Tangent Lines of Parametric Curves