Memorial University of Newfoundland Webpage
Memorial University of Newfoundland Webpage

Mathematics 1001: Calculus II (Winter 2025, online)

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.

On this page, you'll be able to download course handouts (including assignments, tests and solutions). If there is a disruption to the class schedule -- because of weather, for instance -- you should check this page for news relating to modified due dates and the like. Corrections to any errors on assignments or worksheets will also be posted here... although I'll try my best not to make any!

Remember that you can always contact me at

[Your browser cannot view this email address; please turn on JavaScript]

.


News back to top
  • This course has now concluded. Best of luck with your future studies.

General Information back to top

Assignments and Tests back to top

Lectures and Worksheets back to top
  • Welcome to Math 1001!
  • Week 1: Lecture #1 -- Antiderivatives, indefinite integrals, strategy for integration, common integrals including the Power Rule for integrals (Section 1.1)
  • Week 2: Lecture #2 -- Common integrals involving transcendental functions, basic properties of indefinite integrals (Section 1.1)
  • Week 2: Lecture #3 -- Elementary integrals with linear composition, integrals with non-linear composition, the relationship between derivatives and indefinite integrals (Section 1.1)
  • Week 2: Lecture #4 -- Differentials, the method of substitution (Section 1.2)
  • Week 3: Lecture #5 -- Substitution and non-composite integrands, substitution and rational integrands (Section 1.2)
  • Week 3: Lecture #6 -- Long division of polynomials, integrals of tangent, cotangent, secant and cosecant functions (Section 1.2); why integrals do not usually lead to arccosine, arccotangent or arccosecant functions (Section 1.3)
  • Week 3: Lecture #7 -- Integrals leading to inverse trigonometric (arcsine, arctangent and arcsecant) functions, completing the square (Section 1.3)
  • Week 4: Lecture #8 -- Integrals which lead to inverse trigonometric functions after completing the square (Section 1.3); integration by parts (Section 1.4)
  • Week 4: Lecture #9 -- Strategy for integration by parts, integrals which require multiple uses of integration by parts, integration parts applied in the absence of a product, combining integration by substitution and integration by parts (Section 1.4)
  • Week 4: Lecture #10 -- Guidelines for choosing an integration technique, reduction formulas (Section 1.4); the problem of computing the area under a curve (Section 2.1)
  • Week 5: Lecture #11 -- Subintervals and partitions, inscribed and circumscribed rectangles, lower and upper sums (Section 2.1)
  • Week 5: Lecture #12 -- Estimating the area under a curve using n subintervals, sigma notation, summation formulas (Section 2.1)
  • Week 5: Lecture #13 -- Applying the summation formulas, computing lower and upper sums with n subintervals, sample points, area under a curve as the limit of a sum (Section 2.1)
  • Week 6: Lecture #14 -- Irregular partitions, the Riemann sum (Section 2.1); the definite integral (Section 2.2)
  • Week 6: Lecture #15 -- Evaluating definite integrals by finding the limit of a Riemann sum, definite integrals and area, definite integrals with unusual bounds, basic properties of definite integrals, the additive property of intervals for definite integrals (Section 2.2)
  • Week 6: Lecture #16 -- The First Fundamental Theorem of Calculus, applying the First Fundamental Theorem with the Chain Rule, applying the First Fundamental Theorem when the lower bound of the definite integral contains a variable, the Second Fundamental Theorem of Calculus (Section 2.3)
  • Week 7: Lecture #17 -- The proof of the Second Fundamental Theorem of Calculus, applying the Second Fundamental Theorem, improper integrals, the Second Fundamental Theorem and its interaction with the additive interval property (Section 2.3)
  • Week 7: Lecture #18 -- Integration by parts and the Second Fundamental Theorem of Calculus, the method of substitution and the Second Fundamental Theorem (Section 2.3); the area between curves formula (Section 2.4)
  • Week 8: Lecture #19 -- Regions that a naturally bounded by curves, vertically simple regions, regions comprised of several vertically simple regions (Section 2.4)
  • Week 8: Lecture #20 -- Horizontally simple regions, graphing functions of y, when to find area by considering horizontally simple regions (Section 2.4)
  • Week 8: Lecture #21 -- Partial fraction decompositions, partial fractions arising from unique linear factors, repeated linear factors, unique irreducible quadratic factors, and repeated irreducible quadratic factors (Section 3.1)
  • Week 9: Lecture #22 -- Integration by the method of partial fractions, partial fractions and definite integrals, partial fractions and improper rational functions (Section 3.1)
  • Week 9: Lecture #23 -- Sine/cosine integrals with at least one odd power, sine/cosine integrals with only even powers (Section 3.2); trigonometric substitution (Section 3.3)
  • Week 9: Lecture #24 -- Trigonometric substitutions of the tangent, sine and secant functions (Section 3.3)
  • Week 10: Lecture #25 -- Trigonometric substitution and u-substitution, trigonometric substitution and definite integrals (Section 3.3); improper integrals with an infinite upper bound (Sections 3.4)
  • Week 10: Lecture #26 -- Improper integrals with a lower infinite bound, improper integrals with two infinite bounds, infinite regions with finite area, improper integrals with a discontinuity at the lower or upper bounds, improper integrals with a discontinuity on the interval of integration (Section 3.4)
  • Week 10: Lecture #27 -- Improper integrals that require l'Hôpital's Rule (Section 3.4); differential equations, general and particular solutions, initial conditions, initial value problems (Section 4.1)
  • Week 11: Lecture #28 -- Differential equations and kinematics, higher-order differential equations (Section 4.1)
  • Week 11: Lecture #29 -- Separable differential equations, separable equations with implicitly-defined solutions, exponential growth and exponential decay (Section 4.2)
  • Week 11: Lecture #30 -- Examples of exponential growth and decay, applying exponential growth and decay beyond population biology (Section 4.2); the logistic model of population growth (Section 4.3)
  • Week 12: Lecture #31 -- Solutions of the logistic model, dynamics of the logistic model, carrying capacity, equilibrium points, a model for constant harvesting (Section 4.3)
  • Week 12: Lecture #32 -- Solutions of the constant harvesting model (Section 4.3); predator-prey models, the Lotka-Volterra equations and their equilibrium points, models of co-operation and competition between populations (Section 4.4)
  • Week 12: Lecture #33 -- Discrete and continuous random variables, probability density functions, the mean value of a probability density function (Section 4.5)
  • Week 13: Lecture #34 -- Computing the mean value of a probability density function (Section 4.5); volumes of solids of revolution, the Disc-Washer Method (Section 4.6)