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Calculus II: Integrals & Series

Integration and its applications, parametric and polar calculus, and sequences and series — antiderivatives through the Fundamental Theorem, integration techniques, volumes and arc length, and Taylor series.

intermediate Free calculusmathintegralsseries
📖 41 readings ⚡ 41 exercises · 457 min total
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5 modules · 41 lessons
4. The Integral 13 lessons · 172 min
  1. 1 Antiderivatives: running the derivative backwards 13 min
  2. 2 Riemann sums and the area problem 15 min
  3. 3 The definite integral as a limit 15 min
  4. 4 The Fundamental Theorem, part 1: differentiating an area 12 min
  5. 5 The Fundamental Theorem, part 2: evaluating a definite integral 14 min
  6. 6 Substitution 12 min
  7. 7 Integration by parts 13 min
  8. 8 Trigonometric integrals 11 min
  9. 9 Trigonometric substitution 13 min
  10. 10 Partial fractions 12 min
  11. 11 Improper integrals 15 min
  12. 12 Numerical integration 14 min
  13. 13 Choosing a technique 13 min
5. Applications of Integration 8 lessons · 83 min
  1. 14 Area between curves 12 min
  2. 15 Volumes by slicing: disks and washers 10 min
  3. 16 Volumes by cylindrical shells 10 min
  4. 17 Arc length and surfaces of revolution 9 min
  5. 18 Work, force, and hydrostatic pressure 10 min
  6. 19 Center of mass and centroids 11 min
  7. 20 Average value and the Mean Value Theorem for integrals 11 min
  8. 21 Probability densities: integrals as probability 10 min
6. Parametric Curves and Polar Coordinates 4 lessons · 39 min
  1. 22 Parametric curves and their derivatives 9 min
  2. 23 Arc length and area for parametric curves 10 min
  3. 24 Polar coordinates and polar curves 10 min
  4. 25 Area and arc length in polar coordinates 10 min
7. Sequences and Series 10 lessons · 99 min
  1. 26 Sequences and what convergence means 9 min
  2. 27 Monotone, bounded, and the monotone convergence theorem 10 min
  3. 28 Infinite series and partial sums 9 min
  4. 29 Geometric and telescoping series 9 min
  5. 30 Zeno's paradoxes, resolved 12 min
  6. 31 The divergence test and the harmonic series 10 min
  7. 32 The integral test and p-series 10 min
  8. 33 Comparison and limit comparison 10 min
  9. 34 Alternating series; absolute vs. conditional convergence 10 min
  10. 35 The ratio and root tests 10 min
8. Power Series and Taylor Expansions 6 lessons · 64 min
  1. 36 Power series, radius and interval of convergence 11 min
  2. 37 Taylor and Maclaurin series 10 min
  3. 38 Taylor's theorem with remainder: how wrong is the truncation? 11 min
  4. 39 Series in practice: computing e, π, and Euler's formula 10 min
  5. 40 Adv: pointwise vs. uniform convergence of series of functions 12 min
  6. 41 Adv: Fourier series — a first look 10 min

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