Multivariable and Vector Calculus notes
11 notes by 5 users
This GoConqr page gathers notes on Multivariable and Vector Calculus, from navigating three-dimensional space to vector differentiation and Lagrange multipliers. The university-level collection is for students practising these topics and teachers looking for study material. Browse over 10 user-made notes and pick a topic to explore.
Notes
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Vector Functions and Properties of Vector Differentiation We will consider vector functions of a single variable that map from R to Rn, with the domain I being a subset of R and the range being a subset of two or three dimensional space. To differentiate we simply differenti...
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Partial Differentiation - created from Mind Map Total differentials Chain rule Maximum & Minimum
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Week 11 Laplacian intuition Laplacian computation example Explict Laplacian formula Harmonic Functions Laplacian quiz Jacobian prerequisitie knowledge local linearity for a multivariable functions The Jacobian Matrix Computin...
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Unit 1 - created from Mind Map
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this class Unit 1 134 points Week 1 Unit 1 Pre-test 48 points introduction to multivarivble calculus (no quiz) week 2 visualizing scalar-valued functions 14 points week 3 visualizing vector-valued functions 12 points week ...
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week 9 Computing the partial derivative of a vector scaled function Partial Derivative of a paremetric surface part 1 Partial Derivative of a paremtric surface part 2 Partial Derivative of vector feilds Partial Derivative of...
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Week 7 Vector Valued Functions Intro Vector Valued Functions Differentiation Differentiation of a vector valued function vector valued function derivative Vector valued functions quiz Multivariable Chain Rule Multivari...
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Calc 3 Final Study List Lagrange Multipliers with and without constraint curves (max and min) U-V subs and Jacobians Vector Field Conservation, Potential Functions, Work, Fundamental Theorem for Line Integrals Flux and flow on r(t) Outward F...
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Week 10 2d curl intuition 2d curl formula 2d curl example 2d curl nuance Describing rotation in 3d with a vector 3d curl intuition part 1 3d curl intuition part 2 3d curl formula part 1 3d curl formula part 2 3d curl computat...
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week 19 Lagrange Multiplier example part 2 The Lagrangian Meaning of the Lagrange Multiplier Proof of the meaning of Lagrange Multipliers Lagrange Quiz
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Week 15 The Heassian Matrix Expression a quadratic form with a matrix Vector Form of multivariable quadratic approximation quadratic approximation quiz.
More Multivariable and Vector Calculus resources
About multivariable and vector calculus notes
GoConqr OriginalUsing Multivariable and Vector Calculus notes
The notes bring together explanations and study lists on several parts of the unit. You can read about vector functions and differentiation, partial derivatives, curl, the Laplacian and Lagrange multipliers. Calc 3 Final Study List also brings topics such as Jacobians, vector field conservation and flux together in one place.
For an introduction to the material listed here, start with the notes on Unit 1. They cover navigating three-dimensional space, linear functions, cross sections and contour diagrams. If you are working on vector differentiation, Vector Functions and Properties of Vector Differentiation is a more focused starting point.
Revise with notes
Read a section, then write a short summary of the idea or work through an example mentioned in the notes. Return to the relevant section when you need to check a step. For a visual overview, switch to a mind map on the unit page; use a quiz there when you want to check your understanding.
Choose a set of notes and begin with the topic you are studying now.
Frequently asked questions
Which notes should I start with?
Start with the notes on Unit 1 if you want to review navigating three-dimensional space, cross sections and contour diagrams. For a more focused topic, the notes on partial differentiation cover total differentials and the chain rule, among other ideas.
What topics do the weekly notes cover?
The weekly notes cover several topics across the unit. Week 7 includes vector-valued functions and differentiation, while Week 10 covers curl. Week 11 includes the Laplacian, harmonic functions and the Jacobian; Week 15 covers the Hessian matrix and quadratic approximation.
Are these notes free to use?
Yes. Every note listed on this page is free to open and study without an account. The resources were made by GoConqr users, so you can browse the different notes and choose the explanations or study lists that fit the topic you are working on.