Become a Calculus 2 Master

Become a Calculus 2 Master

English | MP4 | AVC 1280×720 | AAC 44KHz 2ch | 32 Hours | 4.39 GB

Learn everything from Calculus 2, then test your knowledge on 355+ quiz questions

HOW BECOME A CALC 2 MASTER IS SET UP TO MAKE COMPLICATED MATH EASY

This 531-lesson course includes video and text explanations of everything in Calculus 2, and it includes more than 175 quizzes (with solutions!) to help you test your understanding along the way. Become a Calculus 2 Master is organized into four sections:

  • Integrals
  • Applications of Integrals
  • Polar & Parametric
  • Sequences & Series

These are four of the most common chapters in every Calculus 2 class.

And here’s what you get inside of every lesson:

Videos: Watch over my shoulder as I solve problems for every single math issue you’ll encounter in class. We start from the beginning… I explain the problem setup and why I set it up that way, the steps I take and why I take them, how to work through the yucky, fuzzy middle parts, and how to simplify the answer when you get it.

Notes: The notes section of each lesson is where you find the most important things to remember. It’s like Cliff Notes for books, but for math. Everything you need to know to pass your class and nothing you don’t.

Quizzes: When you think you’ve got a good grasp on a topic within a course, you can test your knowledge by taking one of our quizzes. If you pass, wonderful. If not, you can review the videos and notes again or ask me for help in the Q&A section.

What Will I Learn?

  • Integrals, including approximating area, the dreaded Fundamental Theorem of Calculus, and every kind of integration technique
  • Applications of Integrals, including volume of revolution with disks, washers and shells, and all kinds of real world applciations
  • Polar & Parametric, including how to sketch polar curves and find the area bounded by polar curves
  • Sequences & Series, including all the convergence tests, and Taylor and Maclaurin series
Table of Contents

Getting started
1 Quick overview before we get underway
2 Download the Calc 2 formula sheet

Integrals – Antiderivatives and indefinite integrals
3 Introduction to antiderivatives and indefinite integrals
4 Introduction to integrals
5 Indefinite integrals
6 Indefinite integrals
7 Properties of integrals
8 Find f given f
9 Find f given f
10 Initial value problems
11 Initial value problems
12 Find f given f and initial conditions

Integrals – Definite integrals
13 Introduction to definite integrals
14 Definite integrals
15 Definite integrals
16 Area under or enclosed by the graph
17 Definite integrals of even and odd functions
18 Definite integrals of even functions
19 Definite integrals of odd functions

Integrals – Riemann sums
20 Introduction to riemann sums
21 Summation notation finding the sum
22 Summation notation expanding
23 Summation notation collapsing
24 Riemann sums
25 Riemann sums left endpoints
26 Riemann sums right endpoints
27 Riemann sums midpoints

Integrals – Other approximation methods
28 Introduction to other approximation methods
29 Over and underestimation
30 Limit process to find area on ab
31 Limit process to find area on -aa
32 Trapezoidal rule
33 Trapezoidal rule
34 Simpsons rule
35 Simpsons rule

Integrals – Error bounds
36 Introduction to error bounds
37 Error bounds
38 Midpoint rule error bound
39 Trapezoidal rule error bound
40 Simpsons rule error bound

Integrals – Fundamental theorem of calculus
41 Introduction to fundamental theorem of calculus
42 Part 1
43 Part 1
44 Part 2
45 Part 2
46 Net change theorem

Integrals – U-substitution
47 Introduction to u-substitution
48 U-substitution
49 U-substitution
50 U-substitution in definite integrals
51 U-substitution in definite integrals

Integrals – Integration by parts
52 Introduction to integration by parts
53 Integration by parts
54 Integration by parts
55 Integration by parts two times
56 Integration by parts two times
57 Integration by parts three times
58 Integration by parts with u-substitution
59 Prove the reduction formula
60 Tabular integration
61 Tabular integration

Integrals – Partial fractions
62 Introduction to partial fractions
63 Partial fractions
64 Distinct linear factors
65 Distinct linear factors example 2
66 Distinct linear factors example 3
67 Distinct quadratic factors
68 Distinct quadratic factors example 2
69 Distinct quadratic factors example 3
70 Repeated linear factors
71 Repeated quadratic factors
72 Repeated quadratic factors example 2
73 Rationalizing substitutions
74 Rationalizing substitutions
75 How to factor a difficult denominator
76 Two ways to find the constants

Integrals – Trigonometric integrals
77 Introduction to trigonometric integrals
78 Trigonometric integrals
79 Trigonometric integrals
80 Trigonometric integrals example 2
81 sinm cosn odd m
82 sinm cosn odd n
83 sinm cosn m and n even
84 tanm secn odd m
85 tanm secn even n
86 tanm secn even n example 2
87 sin(mx) cos(nx)
88 sin(mx) sin(nx)
89 cos(mx) cos(nx)

Integrals – Hyperbolic integrals
90 Introduction to hyperbolic integrals
91 Hyperbolic integrals
92 Hyperbolic integrals
93 Inverse hyperbolic integrals
94 Inverse hyperbolic integrals

Integrals – Trigonometric substitution
95 Introduction to trigonometric substitution
96 Trigonometric substitution
97 Trigonometric substitution setup
98 Trigonometric substitution with secant
99 Trigonometric substitution with sine
100 Trigonometric substitution with sine example 2
101 Trigonometric substitution with tangent
102 Trigonometric substitution with tangent example 2
103 Quadratic functions
104 Quadratic functions

Integrals – Improper integrals
105 Introduction to improper integrals
106 What makes an integral improper
107 Improper integrals
108 Case 1 ainfinity)
109 Case 2 (-infinityb
110 Case 3 (-infinityinfinity)
111 Case 4 (discontinuity at b)
112 Case 5 (discontinuity at a)
113 Case 6 (discontinuity between a and b)
114 Comparison theorem
115 Comparison theorem

Integrals – Reduction formulas
116 Introduction to reduction formulas
117 Integrals using reduction formulas

Applications of Integrals – Area between curves
118 Introduction to area between curves
119 Area between curves
120 Upper and lower curves
121 Left and right curves
122 Sketching the area between curves
123 Dividing the area between curves into equal parts

Applications of Integrals – Arc length
124 Introduction to arc length
125 Arc length
126 Arc length of a curve in the form yf(x)
127 Arc length of a curve in the form xg(y)
128 Arc length using simpsons rule

Applications of Integrals – Average value
129 Introduction to average value
130 Average value
131 Average value
132 Mean value theorem for integrals
133 Mean value theorem for integrals

Applications of Integrals – Surface area of revolution
134 Introduction to surface area of revolution
135 Surface area of revolution
136 Surface area of revolution
137 Surface area of revolution using simpsons ule
138 Surface of revolution equation

Applications of Integrals – Volume of revolution
139 Introduction to volume of revolution
140 Introduction to volume of revolution major axes of revolution
141 Disks
142 Disks horizontal axis
143 Disks vertical axis
144 Disks vertical axis example 2
145 Disks volume of the frustum
146 Washers
147 Washers horizontal axis
148 Washers horizontal axis example 2
149 Washers vertical axis
150 Cylindrical shells
151 Cylindrical shells horizontal axis
152 Cylindrical shells vertical axis
153 Cylindrical shells vertical axis example 2

Applications of Integrals – Work
154 Introduction to work
155 Work done to lift a mass or weight
156 Work done to lift a mass or weight
157 Work done on elastic springs
158 Work done on elastic springs
159 Work done to empty a tank
160 Work done to empty a tank
161 Work done by a variable force
162 Work done by a variable force

Applications of Integrals – Physics
163 Introduction to physics
164 Moments and center of mass of the system
165 Moments of the system
166 Moments of the system x-axis
167 Center of mass of the system
168 Center of mass of the system x-axis
169 Hydrostatic pressure and force
170 Hydrostatic pressure
171 Hydrostatic force
172 Vertical motion
173 Vertical motion
174 Rectilinear motion
175 Rectilinear motion

Applications of Integrals – Geometry
176 Introduction to geometry
177 Centroids of plane regions
178 Centroids of plane regions
179 Centroids of plane regions using simpsons rule
180 Area of the triangle with the given vertices

Applications of Integrals – Economics
181 Introduction to economics
182 Present and future value
183 Single deposit compounded n times future value
184 Single deposit compounded n times present value
185 Single deposit compounded continuously future value
186 Single deposit compounded continuously present value
187 Income stream compounded continuously future value
188 Income stream compounded continuously present value
189 Consumer and producer surplus
190 Consumer and producer surplus

Applications of Integrals – Probability
191 Introduction to probability
192 Probability density
193 Probability density

Applications of Integrals – Biology
194 Introduction to biology
195 Cardiac output
196 Cardiac output using simpsons rule
197 Poiseuilles law
198 Theorem of pappus
199 Theorem of pappus

Polar Parametric – Introduction to parametric curves
200 Introduction to parametric curves
201 Eliminating the parameter
202 Eliminating the parameter
203 Derivative of a parametric curve
204 Derivative of a parametric curve
205 Second derivative of a parametric curve
206 Second derivative of a parametric curve
207 Sketching parametric curves by plotting points
208 Sketching parametric curves by plotting points

Polar Parametric – Calculus with parametric curves
209 Introduction to calculus with parametric curves
210 Tangent line to the parametric curve
211 Tangent line to the parametric curve
212 Area under a parametric curve
213 Area under a parametric curve
214 Area under one arc or loop of a parametric curve
215 Area under one arc or loop of a parametric curve
216 Arc length of a parametric curve
217 Arc length of a parametric curve
218 Arc length particle motion
219 Arc length simpsons rule
220 Surface area of revolution of a parametric curve horizontal axis
221 Surface area of revolution of a parametric curve horizontal axis
222 Surface area of revolution of a parametric curve vertical axis
223 Surface area of revolution of a parametric curve vertical axis
224 Volume of revolution of a parametric curve
225 Volume of revolution of a parametric curve

Polar Parametric – Introduction to polar curves
226 Introduction to polar curves
227 Introduction to polar coordinates
228 Polar coordinates
229 Polar coordinates
230 Converting rectangular equations
231 Converting rectangular equations
232 Converting polar equations
233 Converting polar equations
234 Distance between polar points
235 Distance between polar points
236 Sketching polar curves
237 Sketching polar curves
238 Sketching polar curves from cartesian curves

Polar Parametric – Calculus with polar curves
239 Introduction to calculus with polar curves
240 Tangent line to the polar curve
241 Tangent line to the polar curve
242 Vertical and horizontal tangent lines to the polar curve
243 Vertical and horizontal tangent lines to the polar curve
244 Intersection of polar curves
245 Intersection of polar curves
246 Area inside a polar curve
247 Area inside a polar curve
248 Area bounded by one loop of a polar curve
249 Area bounded by one loop of a polar curve
250 Area between polar curves
251 Area between polar curves
252 Area inside both polar curves
253 Area inside both polar curves
254 Arc length of a polar curve
255 Arc length of a polar curve
256 Arc length of a polar curve example 2
257 Surface area of revolution of a polar curve
258 Surface area of revolution of a polar curve

Sequences Series – Introduction to sequences
259 Introduction to sequences
260 Sequences vs_ series
261 Listing the first terms
262 Calculating the first terms
263 Formula for the general term
264 Formula for the general term
265 Convergence of a sequence
266 Convergence of a sequence
267 Limit of a convergent sequence
268 Limit of a convergent sequence
269 Increasing decreasing and not monotonic
270 Increasing decreasing and not monotonic
271 Bounded sequences
272 Bounded sequences

Sequences Series – Partial sums
273 Introduction to partial sums
274 Calculating the first terms of a series of partial sums
275 Sum of the series of partial sums
276 Sum of the series of partial sums

Sequences Series – Geometric series
277 Introduction to geometric series
278 Geometric series test
279 Geometric series test
280 Sum of the geometric series
281 Sum of the geometric series
282 Values for which the series converges
283 Geometric series for repeating decimals

Sequences Series – Telescoping series
284 Introduction to telescoping series
285 Convergence of a telescoping series
286 Convergence of a telescoping series
287 Sum of a telescoping series
288 Sum of a telescoping series

Sequences Series – Basic convergence tests
289 Introduction to basic convergence tests
290 Recognizing types of series
291 Limit vs_ sum of the series
292 Limit vs_ sum of the series
293 Integral test
294 Integral test
295 p-series test
296 p-series test
297 nth term test
298 nth term test

Sequences Series – Comparison tests
299 Introduction to comparison tests
300 Comparison test
301 Comparison test
302 Limit comparison test
303 Limit comparison test
304 Error or remainder of a series
305 Error or remainder of a series

Sequences Series – Ratio and root tests
306 Introduction to ratio and root tests
307 Ratio test
308 Ratio test
309 Ratio test with factorials
310 Root test
311 Root test
312 Absolute and conditional convergence
313 Absolute and conditional convergence

Sequences Series – Alternating series test
314 Introduction to alternating series test
315 Alternating series test
316 Alternating series test
317 Alternating series estimation theorem
318 Alternating series estimation theorem

Sequences Series – Power series
319 Introduction to power series
320 Power series representation
321 Power series representation
322 Power series multiplication
323 Power series multiplication
324 Power series division
325 Power series division
326 Power series differentiation
327 Power series differentiation
328 Radius and interval of convergence
329 Radius of convergence
330 Interval of convergence
331 Estimating definite integrals
332 Estimating definite integrals
333 Estimating indefinite integrals
334 Estimating indefinite integrals
335 Binomial series
336 Binomial series

Sequences Series – Taylor series
337 Introduction to Taylor series
338 Taylor series
339 Taylor series
340 Radius and interval of convergence of a Taylor series
341 Radius and interval of convergence of a Taylor series
342 Taylors inequality
343 Taylors inequality

Sequences Series – Maclaurin series
344 Introduction to Maclaurin series
345 Maclaurin series
346 Maclaurin series
347 Sum of the Maclaurin series
348 Sum of the Maclaurin series
349 Radius and interval of convergence of a Maclaurin series
350 Radius and interval of convergence of a Maclaurin series
351 Indefinite integral as an infinite series
352 Maclaurin series to estimate an indefinite integral
353 Maclaurin series to estimate a definite integral
354 Maclaurin series to evaluate a limit

Conclusion
355 Wrap-up