CalcIII_LectureWorkbook2017_new.pdf - MATH 25000: Calculus...

This preview shows page 1 - 5 out of 313 pages.

The preview shows page 3 - 5 out of 313 pages.
MATH 25000: Calculus III Lecture NotesDr. Amanda HarsyOctober 17, 20171
We have textbook solutions for you!
/Multivariable-Calculus-11th-Edition-9781337275378-622/
The document you are viewing contains questions related to this textbook.
Chapter 13 / Exercise 61
Multivariable Calculus
Larson
Expert Verified
Contents1Syllabus and Schedule72Sample Gateway193Parametric Equations213.1Calculus with Parametric Equations. . . . . . . . . . . . . . . . . . . . . . .223.2Arc Length. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .233.3ICE 1 -Parametric Equations. . . . . . . . . . . . . . . . . . . . . . . . . .2543-Space274.1Cartesian Coordintates in 3 Space. . . . . . . . . . . . . . . . . . . . . . . .274.2Linear Equations and Traces. . . . . . . . . . . . . . . . . . . . . . . . . . .284.3Parametric Equations in 3 Dimensions. . . . . . . . . . . . . . . . . . . . .295Vectors315.1Introduction to Vectors. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .315.2Displacement Vectors. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .335.3ICE 2 – Vectors. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .355.4Dot Products. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .375.4.1Projections. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .385.5Cross Products. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .405.5.1Torque. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .425.6ICE 3 –Dot and Cross Products. . . . . . . . . . . . . . . . . . . . . . . . .436Vector Valued Functions457Lines and Planes497.1Lines In Space!. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .497.2Planes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .507.3Tangent Lines. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .517.4ICE 4 – Vector Functions. . . . . . . . . . . . . . . . . . . . . . . . . . . . .538Curvature558.1Definitions of Curvature. . . . . . . . . . . . . . . . . . . . . . . . . . . . .558.2Components of Acceleration. . . . . . . . . . . . . . . . . . . . . . . . . . .568.3ICE – Curvature. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .599Surfaces619.1Review of Conic Sections. . . . . . . . . . . . . . . . . . . . . . . . . . . . .619.1.1Parabolas. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .619.1.2Ellipses and Hyperbolas. . . . . . . . . . . . . . . . . . . . . . . . .629.1.3Optional Topic: Translations and Rotations. . . . . . . . . . . . . .662
9.2Graphing Surfaces. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .699.3General Forms of Surfaces. . . . . . . . . . . . . . . . . . . . . . . . . . . .729.4ICE 6 – Surfaces. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .7310 Multivariate Functions7510.1 Functions of Two Variables. . . . . . . . . . . . . . . . . . . . . . . . . . .7510.2 Level Curves and Contour Maps. . . . . . . . . . . . . . . . . . . . . . . . .7610.3 ICE 7 –Level Curves. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .7911 Partial Derivatives8311.1 Higher Partial Derivatives. . . . . . . . . . . . . . . . . . . . . . . . . . . .8411.2 Thinking about Partial Derivatives. . . . . . . . . . . . . . . . . . . . . . .8511.2.1 Partial Derivatives Numerically. . . . . . . . . . . . . . . . . . . . .8511.2.2 Partial Derivatives Verbally. . . . . . . . . . . . . . . . . . . . . . .8511.2.3 Partial Derivatives Graphically. . . . . . . . . . . . . . . . . . . . .8611.3 Visualizing Partial Derivatives with Play-Doh. . . . . . . . . . . . . . . . .8811.4 Ice 8— Partial Derivative Review. . . . . . . . . . . . . . . . . . . . . . . .9912 Polar Coordinates10112.1 Defining Polar Coordinates. . . . . . . . . . . . . . . . . . . . . . . . . . . .10112.2ICE 9 – Polar Coordinates. . . . . . . . . . . . . . . . . . . . . . . . . . .10312.3 Polar Curves. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .10412.4 Graphing Polar Equations. . . . . . . . . . . . . . . . . . . . . . . . . . . .10412.4.1 Circles In Polar Coordinates. . . . . . . . . . . . . . . . . . . . . . .10612.4.2 More Complex Curves In Polar Coordinates. . . . . . . . . . . . . .10612.5 ICE 10 – Polar Graphs. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .10712.6 Derivatives and Tangents Lines in Polar Curves. . . . . . . . . . . . . . . .10812.7 Calculating Polar Areas. . . . . . . . . . . . . . . . . . . . . . . . . . . . .10912.8 Arc Length. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .11112.9 ICE 11 – Polar Calculus. . . . . . . . . . . . . . . . . . . . . . . . . . . . .11313Multivariate Limits and Continuity11513.1 Continuity of Multivariate Functions. . . . . . . . . . . . . . . . . . . . . .11513.2 Evaluating Multivariate Limits. . . . . . . . . . . . . . . . . . . . . . . . .11614 Linear Approximations of the Derivative11914.1 Tangent Plane Revisited. . . . . . . . . . . . . . . . . . . . . . . . . . . . .11914.2 The Differential. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .12015 Differentiability of Multivariate Functions1213
16 The Chain Rule12316.1 Implicit Differentiation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .12516.2ICE 12– Chain Rule. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .12717 Directional Derivatives and Gradient12917.1 Gradient. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .13017.2 Directional Derivatives Definition. . . . . . . . . . . . . . . . . . . . . . . .13118 Optimization13518.1 Max and Mins. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .13518.2 Critical Points. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .13518.3 Using the Contour Map to Classify Critical Points. . . . . . . . . . . . . . .13818.4ICE 13– Optimization. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .13919 Lagrange Multipliers14119.1 Optimizing with Constraints. . . . . . . . . . . . . . . . . . . . . . . . . . .14119.2 2 Constraints. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .14219.3ICE 14– Lagrange Multipliers. . . . . . . . . . . . . . . . . . . . . . . . . .14720Multivariate Integration14920.1 Double Integrals over Rectangular Regions. . . . . . . . . . . . . . . . . . .14920.2 Iterated Integrals over General Regions. . . . . . . . . . . . . . . . . . . . .15120.2.1General (non-rectangular) Regions of Integration. . . . . . . . . . .15120.2.2 Iterated Integrals. . . . . . . . . . . . . . . . . . . . . . . . . . . . .15120.3ICE 15– Iterated Integrals. . . . . . . . . . . . . . . . . . . . . . . . . . . .15320.4Integration over Polar Regions. . . . . . . . . . . . . . . . . . . . . . . . .15521 Applications of Multivariate Integration15721.1 Density and Mass (Optional Topic). . . . . . . . . . . . . . . . . . . . . . .15721.2 Moments of Inertia/ Rotational Inertia (Optional Topic). . . . . . . . . . .16021.3ICE 16 – Mass and Density (Optional Topic). . . . . . . . . . . . . . . . .16321.4 Surface Area. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .16521.5ICE 17– Surface Area. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .16722Triple Integrals16922.1 Triple Integrals in Cartesian Coordinates. . . . . . . . . . . . . . . . . . . .16922.2ICE 18– Triple Integrals. . . . . . . . . . . . . . . . . . . . . . . . . . . . .17322.3Triple Integrals Using Cylindrical and Spherical Coordinates. . . . . . . . .17522.3.1 Cylindrical Coordinates. . . . . . . . . . . . . . . . . . . . . . . . .175

Upload your study docs or become a

Course Hero member to access this document

Upload your study docs or become a

Course Hero member to access this document

End of preview. Want to read all 313 pages?

Upload your study docs or become a

Course Hero member to access this document

We have textbook solutions for you!
The document you are viewing contains questions related to this textbook.
Multivariable Calculus
The document you are viewing contains questions related to this textbook.
Chapter 13 / Exercise 61
Multivariable Calculus
Larson
Expert Verified

  • Left Quote Icon

    Student Picture

  • Left Quote Icon

    Student Picture

  • Left Quote Icon

    Student Picture