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Differential Calculus
MATH 151
Introduction to Limits Estimating Limits numerically Estimating Limits from Graphs Estimating Limits from Graphs Limits at a Point of Discontinuity Determining limits statements T/F Two sided Limits from Graph Two sided Limits from Graph Limit Example 1 Limit Properties Two sided Limits using algebra Limits by Factoring cubic expressions Two sided limits with advaced algebra Limits to define Continuity Limit and Function Defined at point of Discontinuity Fancy Algebra and Limits Defining a Function at a point to make it Continuous Countinuity Limit Examples (Part 1) Limit Examples (Part 2) Limit Examples (Part 3) Limit examples w/ brain matlfuction of first prob More Limits Limits and Infinity Vertical Asmptote of Natural Log Limits at positve and negative infinity Limits with two horizontal asumptotes Limits at Infinity where x is unbounded Squeeze theorem or sandwich theorem Squeeze theorem exercises example MATH 151
Newton, Leibniz, and Usain Bolt Approximating Instantaneous Rate of Change Word Problem Approximating Equation of Tangent Line Word Problem Derivative as Slope of a Tangent Line Tangent Slope as Limiting Value of Secant Slope Example 1 Calculating Slope of Tangent Line Using Derivative Definition Derivatives 1 Formal and Alternative Form of the Derivative Formal and Alternative Form of the Derivative for ln(x) Interpreting Slope of a Curve Exercise Recognizing Slope of Curves Derivative Intuition Module Derivative Intuition Graphs of Functions and Their Derivatives Example 1 Where a Function is Not Differentiable Identifying a Function's Derivative Example Figuring Out Which Function is the Derivative Intuitively Drawing the Derivative of a Function Intuitively Drawing the Anti-derivative of a Function Visualizing Derivatives Exercise Visualizing Derivatives Power Rule (video and quiz) Derivative Properties and Polynomial Derivatives Derivatives of sinx, cosx, tanx, e^x, and lnx Chain Rule Introduction Chain Rule Definition and Example Chain Rule Example Using Visual Function Definitions Chain Rule on Two Functions Chain Rule with Triple Composition Chain Rule on Three Functions Applying the Product Rule for Derivatives Product Rule for More than Two Functions Product Rule Quotient Rule From Product Rule Quotient Rule For Derivative of tanx Quotient Rule Using the Product Rule and the Chain Rule MATH 151 and MATH 251 Implicit Differentiation (video and quiz) Showing Explicit and Implicit Differentiation Give Same Result Implicit Derivative of (x-y)^2=x+y-1 Implicit Derivative of y=cos(5x-3y) Implicit Derivative of (x^2+y^2)^3=5x^2y^2 Finding Slope of Tangent Line with Implicit Differentiation |
MATH 151
Y-Intercept of Tangent Line Example Equation of Tangent Line Example 1 Applications of Derivatives: Tangent and Normal Lines Total Distance Traveled by a Particle Analyzing Particle Movement Based on Graphs When is a Particle Speeding Up Applications of Derivatives: Motion Along a Line Extreme Value Theorem Relative Minima and Maxima Identifying Relative Minimum and Maximum Values Extreme Values from Graphs Minima, Maxima, and Critical Points Testing Critical Points for Local Extrema Identifying Minima and Maxima for x^3 - 12x + 2 Concavity, Concave Upwards and Concave Downwards Intervals Recognizing Concavity Exercise Recognizing Concavity Inflection Points Graphing Using Derivatives Related Rates of Water Pouring into Cone Rate of Change of Distance between Approaching Cars Mean Value Theorem Introduction to L'Hopital's Rule L'Hopital's Rule Example 1 L'Hopital's Rule Example 3 PHYS 218 and CVEN 363 Total Distance Traveled by a Particle Analyzing Particle Movement Based on Graphs When is a Particle Speeding Up Applications of Derivatives: Motion Along a Line Extreme Values from Graphs Rate of Change of Distance between Approaching Cars CVEN 305 Identifying Relative Minimum and Maximum Values Minima, Maxima, and Critical Points Testing Critical Points for Local Extrema Identifying Minima and Maxima for x^3 - 12x + 2 Concavity, Concave Upwards and Concave Downwards Intervals Recognizing Concavity Exercise Recognizing Concavity Inflection Points Graphing Using Derivatives Another Example Graphing with Derivatives CVEN 345 Equation of Normal Line Extreme Value Theorem Relative Minima and Maxima Identifying Relative Minimum and Maximum Values Minima, Maxima, and Critical Points Testing Critical Points for Local Extrema Identifying Minima and Maxima for x^3 - 12x + 2 Concavity, Concave Upwards and Concave Downwards Intervals Recognizing Concavity Exercise Recognizing Concavity Inflection Points Graphing Using Derivatives Another Example Graphing with Derivatives |
Integral Calculus
MATH 151
Antiderivatives and Indefinite Integrals Indefinite Integrals of x Raised to a Power Fundamental Theorem of Calculus Applying the Fundamental Theorem of Calculus MATH 152 Antiderivatives and Indefinite Integrals Indefinite Integrals of x Raised to a Power Antiderivative of x^-1 Basic Trig and Exponential Antiderivatives Simple Riemann Approximation Using Rectangles Generalizing a Left Riemann Sum with Equally Spaced Rectangles Rectangular and Trapezoidal Riemann Approximations Trapezoidal Approximation of Area Under Curve Riemann Sums and Integrals Deriving Integration by Parts Formula Antiderivative of xcosx Using Integration by Parts Integral of lnx Integration by Parts Twice for Antiderivative of (x^2)(e^x) U-Substitution Doing U-Substitution Twice (Second Time with w) U-Substitution and Back Substitution U-Substitution with Definite Integral Intuition for Second Fundamental Theorem of Calculus Evaluating simple Definite Integral Definite Integrals and Negative Area Area between Curves Area between Curves with Multiple Boundaries Introduction to Trig Substitution Integrals: Trig Substitution 1 Trig and U Substitution Together (Part 1) Trig and U Substitution Together (Part 2) Integrals: Trig Substitution 3 (Long Problem) Fundamental Theorem of Calculus Applying the Fundamental Theorem of Calculus Swapping the Bounds for Definite Integral Both Bounds Being a Function of x Introduction to Improper Integrals Improper Integral with Two Infinite Bounds Divergent Improper Integral CVEN 302, CVEN 303 Simple Riemann Approximation Using Rectangles Generalizing a Left Riemann Sum with Equally Spaced Rectangles Rectangular and Trapezoidal Riemann Approximations Trapezoidal Approximation of Area Under Curve Riemann Sums and Integrals CVEN 305, CVEN 363 Antiderivatives and Indefinite Integrals Indefinite Integrals of x Raised to a Power Basic Trig and Exponential Antiderivatives Deriving Integration by Parts Formula Antiderivative of xcosx Using Integration by Parts Integral of lnx Integration by Parts Twice for Antiderivative of (x^2)(e^x) Integration by Parts of (e^x)(cosx) Riemann Sums and Integrals Intuition for Second Fundamental Theorem of Calculus Evaluating simple Definite Integral Definite Integrals and Negative Area Area between Curves Introduciton to Definite Integrals Definite Integrals (Part 2) Definite Integrals (Area Under a Curve) (Part 3) Definite Integrals (Part 4) Definite Integrals (Part 5) Definite Integral with Substitution Fundamental Theorem of Calculus Applying the Fundamental Theorem of Calculus Swapping the Bounds for Definite Integral Both Bounds Being a Function of x Connecting the First and Second Fundamental Theorems of Calculus |
MATH 152
Disk Method Around x-axis Generalizing Disc Method Around x-axis Disc Method Around y-axis Disc Method (Washer Method) for Rotation Around x-axis Disc Method Rotation Around Horizontal Line Washer Method Rotating Around Non-Axis Disc Method Rotating Around Vertical Line Calculating Integral Disc Method Around Verticle Line Washer or Ring Method for Verticle Line Rotation Evaluating Integral for Washer Method Around Verticle Line Shell Method for Rotating Around Verticle Line Shell Method for Rotating Around Horizontal Line Shell Method with Two Functions of x Calculating Integral with Shell Method Shell Method with Two Functions of y Disc Method: Function Rotated About x-Axis Volume of a Sphere Disc Method with Outer and Inner Function Boundaries Shell Method to Rotate Around y-Axis Disc Method: Rotating x=f(y) Around the y-Axis Shell Method Around a Non-Axis Line MATH 152
Explicit and Recursive Definitions of Sequences Finding Terms of Explicitly Defined Sequence Understanding Sequences Geometric Sequence of Progression Geometric Sequences 1 Geometric Sequences 2 Convergent and Divergent Sequences Identifying Sequence Convergence and Divergence Convergence and Divergence of Sequences Definition of Limit of a Sequence and Sequence Convergence Proving a Sequence Converges Sigma Notation for Sums Series as Sum of Sequence Writing a Series in Sigma Notation Explicitly Defining a Series Formula for Arithmetic Series Arithmetic Series Leveraging Properties of Series to Find SumFinding the Sum of n Squares Part 1 Finding the Sum of n Squares Part 2 Alternate Formula for Sum of n Squares Formula for a Finite Geometric Series Sum of an Infinite Geometric Series Geometric Series Convergence and Divergence Examples Repeating Decimal as Infinite Geometric Series Geometric Series of Constants Maclaurin and Taylor Series Intuition Cosine Taylor Series at 0 (Maclaurin) Sine Taylor Series at 0 (Maclaurin) Taylor Series at 0 (Maclaurin) for e to the x Euler's Formula and Euler's Identity Maclaurin Series for sinx, cosx, and e^x Visualizing Taylor Series Approximations Generalized Taylor Series Approximations Error or Remainder of a Taylor Polynomial Approximation STAT 211, CVEN 302 Explicit and Recursive Definitions of Sequences Finding Terms of Explicitly Defined Sequence Geometric Sequence of Progression Convergent and Divergent Sequences Identifying Sequence Convergence and Divergence Definition of Limit of a Sequence and Sequence Convergence Sigma Notation for Sums Series as Sum of Sequence Writing a Series in Sigman Notation Explicity Defining a Series Formula for Arithmetic Series Leveraging Properties of Series to Find Sum Geometric Series Formula for a Finite Geometric Series Sum of an Infinite Geometric Series Geometric Series Convergence and Divergence Examples Euler's Formula and Euler's Identity CVEN 305, CVEN 345 Maclaurin and Taylor Series Intuition Cosine Taylor Series at 0 (Maclaurin) Sine Taylor Series at 0 (Maclaurin) Taylor Series at 0 (Maclaurin) for e to the x |
Multivariable Calculus
MATH 251
Double Integrals 1 Double Integrals 2 Double Integrals 3 Double Integrals 4 Double Integrals 5 Double Integrals 6 Triple Integrals 1 Triple Integrals 2 Triple Integrals 3 MATH 251, MATH 311, and MATH 308
Partial Derivative Partial Derivatives 2 Gradient 1 Gradient 2 Divergence 1 Divergence 2 Divergence 3 Curl 1 Curl 2 Curl 3 PHYS 208, CVEN 363
Conceptual Understanding of Flux in Three Dimensions Constructing a Unit Normal Vector to a Surface Vector Representation of a Surface Integral MATH 251 Introduction to Parametrizing a Surface with Two Parameters Determining a Position Vector-Value Function for a Parametrization of Two Parameters Partial Derivatives of Vector-Valued Functions Introduction to the Surface Integral Example of Calculating a Surface Integral Part 1 Example of Calculating a Surface Integral Part 2 Example of Calculating a Surface Integral Part 3 Conceptual Understanding of Flux in Three Dimensions Constructing a Unit Normal Vector to a Surface Vector Representation of a Surface Integral Stokes' Theorem Intuition Green's and Stokes' Theorem Relationship Orienting Boundary with Surface Orientation and Stokes Conditions for Stokes Theorem Stokes Example Part 1 Stokes Example Part 2: Parameterizing the Surface Stokes Example Part 3: Surface to Double Integral Stokes Example Part 4: Curl and Final Answer Evaluating Line Integral Directly Part 1 Evaluating Line Integral Directly Part 2 MATH 308 Introduction to Parametrizing a Surface with Two Parameters Determining a Position Vector-Value Function for a Parametrization of Two Parameters MATH 311 Partial Derivatives of Vector-Valued Functions Introduction to the Surface Integral Stokes' Theorem Intuition Green's and Stokes' Theorem Relationship Orienting Boundary with Surface Orientation and Stokes Stokes Example Part 1 Stokes Example Part 2: Parameterizing the Surface Stokes Example Part 3: Surface to Double Integral Stokes Example Part 4: Curl and Final Answer Evaluating Line Integral Directly Part 1 Evaluating Line Integral Directly Part 2 |
MATH 251, MATH 311
Introduction to the Line Integral Line Integral Example 2 (part 1) Line Integral Example 2 (part 2) Position Vector Valued Functions Derivative of a Position Vector Valued Function Differential of a Vector Valued Functions Vector Valued Function Derivative Example Green's Theorem Proof (Part 2) Green's Theorem Example 1 Green's Theorem Example 2 Constructing a Unit Normal Vector to a Curve 2D Divergence Theorem MATH 308 Introduction to the Line Integral Line Integral Example 2 (part 1) Line Integral Example 2 (part 2) Position Vector Valued Functions Derivative of a Position Vector Valued Function Differential of a Vector Valued Functions Vector Valued Function Derivative Example Line Integrals and Vector Fields Using a Line Integral to Find the Work Done by a Vector Field Example Parametrization of a Reverse Path Scalar Field Line Integral Independent of Path Direction Vector Field Line Integrals Dependent on Path Direction Path Independence for Line Integrals Closed Curve Line Integrals of Conservative Vector Fields Example of Closed Line Integral of Conservative Field PHYS 218, CVEN 221, CVEN 305, CVEN 363 Introduction to the Line Integral Line Integral Example 1 Line Integral Example 2 (part 1) Line Integral Example 2 (part 2) Position Vector Valued Functions Derivative of a Position Vector Valued Function Differential of a Vector Valued Functions Vector Valued Function Derivative Example Line Integrals and Vector Fields Vector Field Line Integrals Dependent on Path Direction Path Independence for Line Integrals Example of Closed Line Integral of Conservative Field Second Example of Line Integral of Conservative Vector Field MATH 251, MATH 311
3D Divergence Theorem Intuition Divergence Theorem Example 1 Why We Got Zero Flux in Divergence Theorem Example 1 Type I Regions in Three Dimensions Type II Regions in Three Dimensions Type III Regions in Three Dimensions Divergence Theorem Proof (Part 1) Divergence Theorem Proof (Part 2) Divergence Theorem Proof (Part 3) Divergence Theorem Proof (Part 4) Divergence Theorem Proof (Part 5) |
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