Engineering Mathematics

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2 STUDENTS

Contents:
Vector Revision – Intro to curves and vector functions – Limits of vector functions – Calculus of vector functions – Calculus of vector functions tutorial – Vector functions of one variable tutorial – Vector functions tutorial – Intro to functions of two variables – Partial derivatives-2 variable functions: graphs + limits tutorial – Multivariable chain rule and differentiability – Chain rule: partial derivative of $arctan (y/x)$ w.r.t. $x$ – Chain rule: identity involving partial derivatives – Chain rule & partial derivatives – Partial derivatives and PDEs tutorial – Multivariable chain rule tutorial – Gradient and directional derivative – Gradient of a function – Tutorial on gradient and tangent plane – Directional derivative of $f(x,y)$ – Gradient & directional derivative tutorial – Tangent plane approximation and error estimation – Partial derivatives and error estimation – Multivariable Taylor Polynomials – Taylor polynomials: functions of two variables – Differentiation under integral signs: Leibniz rule – Leibniz’ rule: Integration via differentiation under integral sign

Evaluating challenging integrals via differentiation: Leibniz rule – Critical points of functions. Chris Tisdell UNSW Sydney – Second derivative test: two variables. Chris Tisdell UNSW Sydney – How to find critical points of functions – Critical points + 2nd derivative test: Multivariable calculus – Critical points + 2nd derivative test: Multivariable calculus – How to find and classify critical points of functions – Lagrange multipliers – Lagrange multipliers: Extreme values of a function subject to a constraint – Lagrange multipliers example – Lagrange multiplier example: Minimizing a function subject to a constraint – 2nd derivative test, max / min and Lagrange multipliers tutorial – Lagrange multipliers: 2 constraints-Intro to vector fields – What is the divergence – Divergence + Vector fields – Divergence of a vector field: Vector Calculus – What is the curl? Chris Tisdell UNSW Sydney – Curl of a vector field (ex. no.1): Vector Calculus – Line integrals – Integration over curves – Path integral (scalar line integral) from vector calculus

Course Curriculum

Vector Revision: Chris Tisdell UNSW Sydney Details 42:51
Intro to curves and vector functions: Chris Tisdell UNSW Sydney Details 49:7
Limits of vector functions: Chris Tisdell UNSW Sydney Details 44:38
Calculus of vector functions – 1 variable. Chris Tisdell UNSW Sydney Details 20:42
Calculus of vector functions tutorial: Chris Tisdell UNSW Sydney Details 44:25
Vector functions of one variable tutorial. Chris Tisdell UNSW Sydney Details 13:28
Vector functions tutorial. Chris Tisdell UNSW Sydney Details 29:7
Intro to functions of two variables: Chris Tisdell UNSW Sydney Details 33:59
Partial derivatives. Chris Tisdell UNSW Sydney Details 45:48
2 variable functions: graphs + limits tutorial. Chris Tisdell UNSW Sydney Details 41:26
Multivariable chain rule and differentiability: Chris Tisdell UNSW Sydney Details 48:54
Chain rule: partial derivative of $arctan (y/x)$ w.r.t. $x$ Details 5:33
Chain rule: identity involving partial derivatives Details 7:43
Chain rule & partial derivatives Details 9:1
Partial derivatives and PDEs tutorial Details 9:23
Multivariable chain rule tutorial. Chris Tisdell UNSW Sydney Details 33:53
Gradient and directional derivative. Chris Tisdell UNSW Sydney Details 1:7:26
Gradient of a function. Details 14:47
Tutorial on gradient and tangent plane. Chris Tisdell UNSW Sydney Details 22:59
Directional derivative of $f(x,y)$ Details 6:49
Gradient & directional derivative tutorial. Chris Tisdell UNSW Sydney Details 45:41
Tangent plane approximation and error estimation. Chris Tisdell UNSW Sydney Details 28:19
Partial derivatives and error estimation Details 12:21
Multivariable Taylor Polynomials. Chris Tisdell UNSW Sydney Details 54:33
Taylor polynomials: functions of two variables Details 10:44
Differentiation under integral signs: Leibniz rule. Chris Tisdell UNSW Sydney Details 40:35
Leibniz’ rule: Integration via differentiation under integral sign Details 5:39
Evaluating challenging integrals via differentiation: Leibniz rule Details 8:3
Critical points of functions. Chris Tisdell UNSW Sydney Details 30:42
Second derivative test: two variables. Chris Tisdell UNSW Sydney Details 27:10
How to find critical points of functions Details 14:40
Critical points + 2nd derivative test: Multivariable calculus Details 7:17
Critical points + 2nd derivative test: Multivariable calculus Details 7:17
How to find and classify critical points of functions Details 11:58
Lagrange multipliers. Chris Tisdell UNSW Sydney. Details 45:23
Lagrange multipliers: Extreme values of a function subject to a constraint Details 7:31
Lagrange multipliers example Details 11:8
Lagrange multiplier example: Minimizing a function subject to a constraint Details 8:29
2nd derivative test, max / min and Lagrange multipliers tutorial. Chris Tisdell UNSW Sydney Details 42:38
Lagrange multipliers: 2 constraints. Chris Tisdell UNSW Sydney Details 14:24
Intro to vector fields. Chris Tisdell UNSW Sydney Details 20:7
What is the divergence? Chris Tisdell UNSW Sydney Details 41:50
Divergence + Vector fields. Chris Tisdell UNSW Sydney Details 13:37
Divergence of a vector field: Vector Calculus Details 6:21
What is the curl? Chris Tisdell UNSW Sydney Details 39:45
Curl of a vector field (ex. no.1): Vector Calculus Details 5:22
Curl of a vector field (ex. no.2): Vector calculus Details 8:38
Line integrals. Chris Tisdell UNSW Sydney Details 16:7
Integration over curves. Chris Tisdell UNSW Sydney Details 45:38
Path integral (scalar line integral) from vector calculus Details 6:15

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