Concordia MATH 203 Calculus I: Syllabus, Topics and Practice

MATH 203 is Differential and Integral Calculus I at Concordia University in Montreal, the first of two connected calculus courses. It is the calculus course many students take to complete a prerequisite, for example in the Extended Credit Program or before computer science and engineering courses. This guide maps every MATH 203 topic to free practice so you can learn each idea by solving problems with instant feedback.

What Concordia MATH 203 covers

The Concordia undergraduate calendar describes MATH 203 as an overview of functions and limits; the derivative as rate of change; differentiation of elementary functions (power, exponential, logarithmic, trigonometric); differentiation rules (product, quotient and chain rules); implicit differentiation; higher derivatives; and approximations using linearization and the differential. Applications include related rates, optimization, analysis of functions (maxima, minima and inflection points) and graphing. It is a 3-credit course with lectures and tutorials, and the prerequisite is MATH 201 or equivalent.

Compared with a typical Calculus 1, MATH 203 covers the differential half only. Antiderivatives, definite integrals and the Fundamental Theorem of Calculus are all in MATH 205.

MATH 203 topic map

MATH 203 in the Concordia sequence

Example problems at the MATH 203 level

1. Implicit differentiation. For x^2 + y^2 = 25, differentiate both sides: 2x + 2yy' = 0, so y' = -\frac{x}{y}. At (3, 4) the slope is -\frac{3}{4}.

2. Related rates. A circle's radius grows at 2 cm/s. With A = \pi r^2, \frac{dA}{dt} = 2\pi r\frac{dr}{dt}, so when r = 5 the area grows at 20\pi cm²/s.

3. Linearization. Near x = 4, \sqrt{x} \approx 2 + \frac{1}{4}(x - 4), so \sqrt{4.1} \approx 2.025.

4. Inflection points. For f(x) = x^3 - 3x, f''(x) = 6x changes sign at x = 0, so (0, 0) is an inflection point.

How to do well in MATH 203

• Refresh MATH 201 skills. Functions, exponents, logs and trig identities appear in every derivative. Our warm-up practice is a quick check.
• Practise rules in mixed sets. Exams combine the product, quotient and chain rules in one problem.
• Follow a recipe for word problems. Draw, name variables, write the equation, differentiate, then substitute numbers last.
• Use your tutorial. The calendar lists a tutorial component, which is the best place to get unstuck.

Tip: in related rates, substitute the given numbers only after you differentiate. Plugging in too early turns variables into constants.