In English Vectors in space: the three products, 201-SN4-RE
Two sets of direct calculations, ten norms, dot products and angles and eight cross and scalar triple products; then components and norm in space, dot product and projection, cross product and areas, scalar triple product and volumes, then an exam-level part: Lagrange's identity, the coplanarity criterion and a complete tetrahedron solved by two methods. Also direction angles and direction cosines with the identity cos²α+cos²β+cos²γ=1 and its trap (no vector is at 45° from all three axes), the orthogonal decomposition of a vector and the distance from a point to a line computed by two matching methods, the vector triple product (BAC minus CAB rule) and the non-associativity of the cross product, and two skew lines classified then measured with the scalar triple product. A Part C adds five classics: the cube in coordinates, a parallelogram in space, decomposing a vector with scalar triple products, the tetrahedral angle of methane and the power received by a tilted solar panel.
17 corrected exercises • 170 points
In English Functions, domains and operations, 201-SN2-RE
The opening chapter of differential calculus, the one the rest of the course depends on: the only three restrictions that build a domain, a root in the denominator and its strict inequality, a sum of two absolute values read as a sum of distances, the intersection of domains and the zeros of the denominator to remove, composition and its domain built in two steps, transformations of a graph and the order that makes them non-commutative, inverse functions and the swap of domain and range, the unit circle through reference angles, and two modelling problems where the physical domain decides whether the answer is valid. A Part C adds five classics: the domain by a sign chart, logarithm and exponential, inverse trigonometric functions, the spreading slick and the arched tunnel.
17 corrected exercises • 170 points
In English Limits and continuity, 201-SN2-RE
Reading left-hand and right-hand limits from the graph of a function with a jump and a hole, indeterminate forms resolved by factoring and by the conjugate, limits at infinity with horizontal and oblique asymptotes and the trap of the TWO asymptotes of a square root, continuity of piecewise functions and the classification of discontinuities, the Intermediate Value Theorem with the bisection method, and trigonometric limits with the Squeeze Theorem. Also covered: the limit laws and their false converse, substitution in a limit and the counterexample where the composite fails, the formal epsilon-delta definition with two complete proofs, and the Extreme Value Theorem with each of its three hypotheses shown to be essential. A Part C adds five classics: parameters that make a function continuous, the floor function, limits of transcendental functions, the learning curve and the cost of pollution removal.
17 corrected exercises • 170 points
In English Continuity at a point: practice bank, 201-SN2-RE
Two banks of functions to settle one at a time, is it continuous at a: six you can decide in your head, then eight with sine over x, the conjugate, the edge of the domain, e to the power one over x and the Squeeze Theorem. Then spotting the suspicious points and stating where a function is continuous, six holes to fill by continuous extension, five parameters to set, one of which admits two values and one none. Exam-level part: the sign of infinite one-sided limits and absolute values removed on the correct side, eight indeterminate forms and their techniques, five statements to correct, the joint of a playground slide where continuity is not enough to remove the corner, and a parking rate charged per hour or part of an hour, with its three-dollar jumps. Questions from a first CEGEP midterm are built in: a sum of cubes and polynomial division, absolute values removed on the correct side, a parameter that decides between continuity, a displaced value and a jump, a squared denominator to cancel twice, and the squeeze whose inequalities reverse on the left.
10 corrected exercises • 100 points
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