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Calculus 3 (Multivariable) Masterclass

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Course overview

Learn multivariable calculus with this Calculus 3 (Multivariable) Masterclass course. In this course, you will understand the complexities of multivariable calculus and solve various problems.

The  Calculus 3 (Multivariable) Masterclass course will go over the fundamental ideas about multivariable functions. It will introduce you to analytical geometry and explain where it’s used. You will identify the distance formula to calculate distance between two points and learn how to calculate dot and cross products. In addition, you will learn about conic sections, topology, partial derivatives and vector-valued functions and use them to solve problems. Many practice problems with solutions are included in this course to improve your problem-solving abilities.

Learning outcomes

  • Learn about limit, continuity and differentiability
  • Know how to graph a parabola using conic sections
  • Understand what is a paraboloid in calculus
  • Identify the differentiation rules and use them to solve problems
  • Learn about different coordinate systems
  • Be able to compute a composite function’s derivative using chain rule
  • Learn how to use Taylor’s formula

Who Is This Course For?

Anyone interested in learning Calculus most efficiently can take this Calculus 3 (Multivariable) Masterclass course. The skills gained from this training will provide excellent opportunities for career advancement.

Entry Requirement

  • This course is available to all learners of all academic backgrounds.
  • Learners should be aged 16 or over.
  • Good understanding of English language, numeracy and ICT skills are required to take this course.

Certification

  • After you have successfully completed the course, you will obtain an Accredited Certificate of Achievement. And, you will also receive a Course Completion Certificate following the course completion without sitting for the test. Certificates can be obtained either in hardcopy for £39 or in PDF format at the cost of £24.
  • PDF certificate’s turnaround time is 24 hours, and for the hardcopy certificate, it is 3-9 working days.

Why Choose Us?

  • Affordable, engaging & high-quality e-learning study materials;
  • Tutorial videos and materials from the industry-leading experts;
  • Study in a user-friendly, advanced online learning platform;
  • Efficient exam systems for the assessment and instant result;
  • United Kingdom & internationally recognized accredited qualification;
  • Access to course content on mobile, tablet and desktop from anywhere, anytime;
  • Substantial career advancement opportunities;
  • 24/7 student support via email.

Career Path

The Calculus 3 (Multivariable) Masterclass  course provides  essential skills that will make you more effective in your role. It would be beneficial for any related profession in the industry, such as:

  • Math’s Teacher

Course Curriculum

Unit 1 - About the course
Introduction to the course 00:30:00
Unit 2 - Analytical geometry in the space
The plane R^2 and the 3-space R^3: points and vectors 00:25:00
Distance between points 00:08:00
Vectors and their products 00:04:00
Dot product 00:14:00
Cross product 00:13:00
Scalar triple product 00:07:00
Describing reality with numbers; geometry and physics 00:06:00
Straight lines in the plane 00:08:00
Planes in the space 00:13:00
Straight lines in the space 00:08:00
Unit 3 - Conic Units: circle, ellipse, parabola, hyperbola
Conic Units, an introduction 00:06:00
Quadratic curves as conic Units 00:10:00
Definitions by distance 00:17:00
Cheat sheets 00:04:00
Circle and ellipse, theory 00:19:00
Parabola and hyperbola, theory 00:12:00
Completing the square 00:04:00
Completing the square, problems 1 and 2 00:12:00
Completing the square, problem 3 00:10:00
Completing the square, problems 4 and 5 00:08:00
Completing the square, problems 6 and 7 00:08:00
Unit 4 - Quadric surfaces: spheres, cylinders, cones, ellipsoids, paraboloids etc
Quadric surfaces, an introduction 00:16:00
Degenerate quadrics 00:17:00
Ellipsoids 00:08:00
Paraboloids 00:16:00
Hyperboloids 00:25:00
Problems 1 and 2 00:09:00
Problem 3 00:07:00
Problems 4 and 5 00:10:00
Problem 6 00:06:00
Unit 5 - Topology in R^n
Neighborhoods 00:07:00
Open, closed, and bounded sets 00:14:00
Identify sets, an introduction 00:04:00
Example 1 00:06:00
Example 2 00:06:00
Example 3 00:05:00
Example 4 00:06:00
Example 5 00:04:00
Example 6 and 7 00:06:00
Unit 6 - Coordinate systems
Different coordinate systems 00:02:00
Polar coordinates in the plane 00:11:00
An important example 00:07:00
Solving 3 problems 00:19:00
Cylindrical coordinates in the space 00:03:00
Problem 1 00:03:00
Problem 2 00:02:00
Problem 3 00:04:00
Problem 4 00:04:00
Spherical coordinates in the space 00:08:00
Some examples 00:08:00
Conversion 00:08:00
Problem 1 00:08:00
Problem 2 00:12:00
Problem 3 00:11:00
Problem 4 00:07:00
Unit 7 - Vector-valued functions, introduction
Curves: an introduction 00:10:00
Functions: repetition 00:08:00
Functions: repetition 00:08:00
Vector-valued functions, parametric curves: domain 00:08:00
Unit 8 - Some examples of parametrisation
Vector-valued functions, parametric curves 00:11:00
An intriguing example 00:14:00
Problem 1 00:12:00
Problem 2 00:13:00
Problem 3 00:15:00
Problem 4, helix 00:09:00
Unit 9 - Vector-valued calculus; curve: continuous, differentiable, and smooth
Notation 00:05:00
Limit and continuity 00:09:00
Derivatives 00:14:00
Speed, acceleration 00:08:00
Position, velocity, acceleration: an example 00:06:00
Smooth and piecewise smooth curves 00:09:00
Sketching a curve 00:15:00
Sketching a curve: an exercise 00:16:00
Example 1 00:11:00
Example 2 00:16:00
Example 3 00:10:00
Extra theory: limit and continuity 00:19:00
Extra theory: derivative, tangent, and velocity 00:13:00
Differentiation rules 00:27:00
Differentiation rules, example 1 00:19:00
Differentiation rules: example 2 00:19:00
Position, velocity, acceleration, example 3 00:15:00
Position and velocity, one more example 00:15:00
Trajectories of planets 00:13:00
Unit 10 - Arc length
Parametric curves: arc length 00:15:00
Arc length: problem 1 00:11:00
Arc length: problems 2 and 3 00:15:00
Arc length: problems 4 and 5 00:13:00
Unit 11 - Arc length parametrisation
Parametric curves: parametrisation by arc length 00:10:00
Parametrisation by arc length, how to do it, example 1 00:12:00
Parametrisation by arc length, example 2 00:22:00
Arc length does not depend on parametrisation, theory 00:14:00
Unit 12 - Real-valued functions of multiple variables
Functions of several variables, introduction 00:09:00
Introduction, continuation 1 00:14:00
Introduction, continuation 2 00:08:00
Domain 00:06:00
Domain, problem solving part 1 00:18:00
Domain, problem solving part 2 00:13:00
Domain, problem solving part 3 00:15:00
Functions of several variables, graphs 00:14:00
Plotting functions of two variables, problems part 1 00:16:00
Plotting functions of two variables, problems part 2 00:12:00
Level curves 00:14:00
Level curves, problem 1 00:10:00
Level curves, problem 2 00:08:00
Level curves, problem 3 00:09:00
Level curves, problem 4 00:14:00
Level curves, problem 5 00:16:00
Level surfaces, definition and problem solving 00:20:00
Unit 13 - Limit, continuity
Limit and continuity, part 1 00:18:00
Limit and continuity, part 2 00:15:00
Limit and continuity, part 3 00:20:00
Problem solving 1 00:25:00
Problem solving 2 00:18:00
Problem solving 3 00:20:00
Problem solving 4 00:15:00
Unit 14 - Partial derivative, tangent plane, normal line, gradient, Jacobian
Introduction 1: definition and notation 00:10:00
Introduction 2: arithmetical consequences 00:12:00
Introduction 3: geometrical consequences (tangent plane) 00:13:00
Introduction 4: partial derivatives not good enough 00:06:00
Introduction 5: a pretty terrible example 00:15:00
Tangent plane, part 1 00:07:00
Normal vector 00:15:00
Tangent plane part 2: normal equation 00:09:00
Normal line 00:08:00
Tangent planes, problem 1 00:14:00
Tangent planes, problem 2 00:13:00
Tangent planes, problem 3 00:16:00
Tangent planes, problem 4 00:09:00
Tangent planes, problem 5 00:11:00
The gradient 00:11:00
A way of thinking about functions from R^n to R^m 00:11:00
The Jacobian 00:14:00
Unit 15 - Higher partial derivatives
Introduction 00:15:00
Definition and notation 00:07:00
Mixed partials, Hessian matrix 00:13:00
The difference between Jacobian matrices and Hessian matrices 00:08:00
Equality of mixed partials; Schwarz’ theorem 00:09:00
Schwarz’ theorem: Peano’s example 00:06:00
Schwarz’ theorem: the proof 00:19:00
Partial Differential Equations, introduction 00:04:00
Partial Differential Equations, basic ideas 00:11:00
Partial Differential Equations, problem solving 00:13:00
Laplace equation and harmonic functions 1 00:08:00
Laplace equation and harmonic functions 2 00:06:00
Laplace equation and Cauchy-Riemann equations 00:11:00
Dirichlet problem 00:07:00
Unit 16 - Chain rule: different variants
A general introduction 00:17:00
Variants 1 and 2 00:10:00
Variant 3 00:18:00
Variant 3 (proof) 00:11:00
Variant 4 00:09:00
Example with a diagram 00:04:00
Problem solving 00:08:00
Problem solving, problem 1 00:04:00
Problem solving, problem 2 00:09:00
Problem solving, problem 3 00:33:00
Problem solving, problem 4 00:15:00
Problem solving, problem 5 00:28:00
Problem solving, problem 6 00:09:00
Problem solving, problem 7 00:06:00
Problem solving, problem 8 00:18:00
Unit 17 - Linear approximation, linearisation, differentiability, differential
Linearisation and differentiability in Calc1 00:11:00
Differentiability in Calc3: introduction 00:15:00
Differentiability in two variables, an example 00:10:00
Differentiability in Calc3 implies continuity 00:10:00
Partial differentiability does NOT imply differentiability 00:05:00
An example: continuous, not differentiable 00:06:00
Differentiability in several variables, a test 00:18:00
Differentiability, Partial Differentiability, and Continuity in Calc3 00:12:00
Differentiability in two variables, a geometric interpretation 00:11:00
Linearization: two examples 00:16:00
Linearization, problem solving 1 00:11:00
Linearization, problem solving 2 00:11:00
Linearization, problem solving 3 00:12:00
Linearization by Jacobian matrix, problem solving 00:16:00
Differentials: problem solving 1 00:11:00
Differentials: problem solving 2 00:10:00
Unit 18 - Gradient, directional derivatives
Gradient 00:04:00
The gradient in each point is orthogonal to the level curve through the point 00:08:00
The gradient in each point is orthogonal to the level surface through the point 00:14:00
Tangent plane to the level surface, an example 00:06:00
Directional derivatives, introduction 00:06:00
Directional derivatives, the direction 00:04:00
How to normalize a vector and why it works 00:08:00
Directional derivatives, the definition 00:07:00
Partial derivatives as a special case of directional derivatives 00:05:00
Directional derivatives, an example 00:11:00
Directional derivatives: important theorem for computations and interpretations 00:10:00
Directional derivatives: an earlier example revisited 00:05:00
Geometrical consequences of the theorem about directional derivatives 00:10:00
Geometical consequences of the theorem about directional derivatives, an example 00:07:00
Directional derivatives, an example 00:11:00
Normal line and tangent line to a level curve: how to get their equations 00:06:00
Normal line and tangent line to a level curve: their equations, an example 00:14:00
Gradient and directional derivatives, problem 1 00:18:00
Gradient and directional derivatives, problem 2 00:20:00
Gradient and directional derivatives, problem 3 00:09:00
Gradient and directional derivatives, problem 4 00:04:00
Gradient and directional derivatives, problem 5 00:12:00
Gradient and directional derivatives, problem 6 00:10:00
Gradient and directional derivatives, problem 7 00:13:00
Unit 19 - Implicit functions
What is the Implicit Function Theorem? 00:13:00
Jacobian determinant 00:04:00
Jacobian determinant for change to polar and to cylindrical coordinates 00:07:00
Jacobian determinant for change to spherical coordinates 00:09:00
Jacobian determinant and change of area 00:10:00
The Implicit Function Theorem variant 1 00:08:00
The Implicit Function Theorem variant 1, an example 00:15:00
The Implicit Function Theorem variant 2 00:10:00
The Implicit Function Theorem variant 2, example 1 00:07:00
The Implicit Function Theorem variant 2, example 2 00:14:00
The Implicit Function Theorem variant 3 00:15:00
The Implicit Function Theorem variant 3, an example 00:12:00
The Implicit Function Theorem variant 4 00:11:00
The Inverse Function Theorem 00:09:00
The Implicit Function Theorem, summary 00:04:00
Notation in some unclear cases 00:08:00
The Implicit Function Theorem, problem solving 1 00:27:00
The Implicit Function Theorem, problem solving 2 00:13:00
The Implicit Function Theorem, problem solving 3 00:07:00
The Implicit Function Theorem, problem solving 4 00:16:00
Unit 20 - Taylor’s formula, Taylor’s polynomial, quadratic forms
Taylor’s formula, introduction 00:10:00
Quadratic forms and Taylor’s polynomial of second degree 00:22:00
Taylor’s polynomial of second degree, theory 00:11:00
Taylor’s polynomial of second degree, example 1 00:07:00
Taylor’s polynomial of second degree, example 2 00:04:00
Taylor’s polynomial of second degree, example 3 00:11:00
Classification of quadratic forms (positive definite etc) 00:12:00
Classification of quadratic forms, problem solving 1 00:08:00
Classification of quadratic forms, problem solving 2 00:14:00
Classification of quadratic forms, problem solving 3 00:10:00
Unit 21 - Optimization on open domains (critical points)
Extreme values of functions of several variables 00:12:00
Extreme values of functions of two variables, without computations 00:10:00
Critical points and their classification (max, min, saddle) 00:09:00
Second derivative test for C^3 functions of several variables 00:12:00
Second derivative test for C^3 functions of two variables 00:06:00
Critical points and their classification: some simple examples 00:06:00
Critical points and their classification: more examples 1 00:05:00
Critical points and their classification: more examples 2 00:08:00
Critical points and their classification: more examples 3 00:10:00
Critical points and their classification: a more difficult example (4) 00:47:00
Unit 22 - Optimization on compact domains
Extreme values for continuous functions on compact domains 00:06:00
Eliminate a variable on the boundary 00:10:00
Parameterize the boundary 00:08:00
Unit 23 - Lagrange multipliers (optimization with constraints)
Lagrange multipliers 1 00:13:00
Lagrange multipliers 1, an old example revisited 00:08:00
Lagrange multipliers 1, another example 00:13:00
Lagrange multipliers 2 00:10:00
Lagrange multipliers 2, an example 00:18:00
Lagrange multipliers 3 00:08:00
Lagrange multipliers 3, an example 00:09:00
Summary: optimization 00:07:00
Unit 24 - Final words
The last one 00:05:00

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