Memorial University of Newfoundland Webpage
Memorial University of Newfoundland Webpage

Mathematics 1001: Calculus II (Fall 2019)

Mathematics 1001 is a direct sequel to Mathematics 1000, and serves as an introduction to integral calculus. It begins by introducing the concept of the antiderivative and basic techniques for indefinite integration. The definite integral is then developed by way of Riemann sums and the Fundamental Theorem of Calculus. Advanced integration techniques are studied, before the course concludes by considering some applications of integration (such as simple differential equations, and area and volume problems). In order to do well, it is essential that students be comfortable with all aspects of differentiation from Math 1000.

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  • This course has now concluded. Best of luck with your future studies.

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I do not make lecture notes available outside of class; if you miss a lecture for any reason, I strongly encourage you to borrow the corresponding notes from a classmate. However, as a guide, here is a brief summary of what was covered in each lecture.
  • September 6th: Antiderivatives, indefinite integrals, elementary indefinite integrals (Section 1.1)
  • September 9th: Basic properties of indefinite integrals, elementary integrals with linear composition (Section 1.1)
  • September 11th: Integrals with non-linear composition (Section 1.1); differentials, the method of substitution (Section 1.2)
  • September 13th: Substitution and more complicated integrands, substitution and non-composite integrands, substitution and rational integrands, long division of polynomials (Section 1.2)
  • September 16th: Integrals of tangent, cotangent, secant and cosecant functions (Section 1.2); integrals leading to inverse trigonometric (arcsine, arctangent and arcsecant) functions (Section 1.3)
  • September 18th: Completing the square, integrals which lead to inverse trigonometric functions after completing the square (Section 1.3)
  • September 20th: Integration by parts, integrals which require multiple uses of integration by parts (Section 1.4)
  • September 23rd: Criteria for setting up integration by parts, when the original integral recurs while using integration by parts, combining integration by substitution and integration by parts (Section 1.4)
  • September 25th: Reduction formulas (Section 1.4); the problem of computing the area under a curve, subintervals and partitions (Section 2.1)
  • September 27th: Lower and upper sums, sigma notation (Section 2.1)
  • September 30th: Properties of sigma notation, summation formulas, computing lower and upper sums with n subintervals (Section 2.1)
  • October 2nd: Sample points, area under a curve as the limit of a Riemann sum, irregular partitions (Section 2.1); the definite integral (Section 2.2)
  • October 4th: Evaluating definite integrals by finding the limit of a Riemann sum, definite integrals with unusual bounds, basic properties of definite integrals, the additive property of intervals for definite integrals (Section 2.2)
  • October 7th: The First Fundamental Theorem of Calculus (Section 2.3)
  • October 9th: Improper integrals, the First Fundamental Theorem of Calculus and its interaction with the additive property of definite integrals, integration by parts and the First Fundamental Theorem, integration by substitution and the First Fundamental Theoem (Section 2.3)
  • October 11th: The Second Fundamental Theorem of Calculus (Section 2.3); computing the area between curves (Section 2.4)
  • October 18th: Vertically simple regions, regions comprised of vertically simple regions, horizontally simple regions (Section 2.4)
  • October 21st: Converting a region comprised of vertically simple regions into a horizontally simple region (Section 2.4)
  • October 23rd: Finding area by integrating with respect to y to simplify the integral, graphing functions of y directly (Section 2.4); the method of partial fractions, partial fractions with unique and repeated linear factors in the denominator (Section 3.1)
  • October 25th: Partial fractions with unique and repeated irreducible quadratic factors in the denominator (Section 3.1)
  • October 28th: Alternative method for finding the constants in the partial fraction decomposition, partial fractions and improper rational functions, partial fractions and definite integrals (Section 3.1); overall strategy for trigonometric integrals (Section 3.2)
  • October 30th: Sine/cosine and tangent/secant integrals (Section 3.2)
  • November 1st: Cotangent/cosecant integrals, integrals involving other trigonometric combinations (Section 3.2); overall strategy for trigonometric substition (Section 3.3)
  • November 4th: Trigonometric substitutions of tangent, sine and cosecant (Section 3.3)
  • November 6th: Trigonometric substitution with u-substitution, trigonometric substitution and completing the square (Section 3.3); strategies for integration (Section 3.4)
  • November 8th: Improper integrals with one or two infinite bounds, improper integrals with a discontinuity at the lower bound (Section 3.5)
  • November 15th: Improper integrals with a discontinuity at the upper bound or on the interval of integration, improper integrals requiring l'Hopital's Rule (Section 3.5); differential equations, general solutions, initial conditions, particular solutions (Section 4.1)
  • November 18th: Differential equations and kinematics problems (Section 4.1); separable equations, exponential growth and decay (Section 4.2)
  • November 20th: Applying the exponential growth/decay equation, Newton's Law of Cooling (Section 4.2)
  • November 22nd: Applying Newton's Law of Cooling (Section 4.2); solids of revolution, volume by the disc method (Section 4.3)
  • November 25th: Volume by the disc method for vertical axes of revolution, the disc-washer method (Section 4.3)
  • November 27th: The disc-washer method for vertical axes of revolution (Section 4.3); the shell method (Section 4.4)
  • November 29th: Choosing between the disc-washer method and the shell method (Section 4.4)