Multivariable Calculus Full Year (Two Semesters) Prerequisite: Calculus Honors or equivalent, successful
Calculus Full Year (Two Semesters)
Prerequisites: Precalculus or equivalent OR best-fit mathematical placement
completion of honors prerequisites OR best-fit mathematical placement
This course is designed to provide a solid foundation in both differential and integral calculus. Students will learn to evaluate limits and assess function continuity both analytically and graphically, and they will utilize this understanding to uncover the limit-based definition of the first derivative. As the year progresses, students will delve into the many techniques of differentiation, and explore a variety of applications in the form of optimization and related rates problems. The second half of the year will be spent focusing on integration, the techniques thereof, and applications to the calculation of area and volume. Topics from algebra and trigonometry are reviewed throughout the course, and students will have the opportunity to revisit previously learned concepts and problems through a calculus- based lens. Topics will be presented graphically, algebraically, and numerically, and real-world applications will be explored whenever possible. Texts and Materials: Graphing calculator; Calculus: Graphical, Numerical, Algebraic, Pearson, by Finney, Ross, 3RD 10 ISBN-10: 0-13-368839-9, ISBN-13: 978-0-13-368839-9 Honors Calculus Full Year (Two Semesters) Prerequisites: Precalculus or equivalent, successful
This course allows students to continue their study of calculus at an accelerated level. Having learned how to evaluate limits, derivatives, and integrals of single- variable functions, students will now study those same concepts in the context of vectors and multivariable functions. Students will also learn the many facets of sequences and series, as well as build upon their
understanding of differential equations. Texts and Materials: Graphing calculator;
Calculus: Graphical, Numerical, Algebraic, Pearson, by Finney, Ross, 3RD 10 ISBN-10: 0-13-368839-9, ISBN-13: 978-0-13-368839-9 Fundamentals of Integrated Mathematics 1 Full Year (Two Semesters) Prerequisites: Recommendation of Student Support Services This course is designed to hone the foundational skills needed to be successful in algebra, geometry, and statistics. Topics include number systems and operations, properties of numbers, proportional thinking, properties and classification of geometric figures, measurement, Pythagorean relationships, data analysis, probability, simplifying and solving algebraic equations, patterns, and functions. Additionally, the Standards for Mathematical Practices (making sense of problems and persevering in solving them, reasoning abstractly and quantitatively, constructing viable arguments and critiquing the reasoning of others, modeling with mathematics, using appropriate tools strategically, attending to precision, looking for and making use of structure, and looking for and expressing regularity in repeated reasoning) are woven into the activities and assessments throughout the course. Designed to have a low student to teacher ratio, this course is focused on making arithmetic and algebraic concepts approachable and accessible for students who are building their foundational math skills.
completion of honors prerequisites OR best-fit mathematical placement
This course will provide a comprehensive investigation of both differential and integral calculus. Topics of study include limits and continuity, differentiation, integration, and the techniques and applications thereof. Additional topics such as partial fractions and L’Hopital’s Rule will also be introduced, and topics from precalculus - inequalities, functions, trigonometry, and logarithms - will be reviewed throughout. The course stresses the importance of critical thinking, and all problems will be approached from algebraic, graphical, and numerical perspectives. Real-world applications to business, engineering, and population growth will be explored, and students will be regularly encouraged to draw their own hypotheses and conjectures, and to speak and write in the language of mathematics in order to justify the veracity of their claims. Texts and Materials: Graphing calculator; Calculus: Graphical, Numerical, Algebraic, Pearson, by Finney, Ross, 3RD 10 ISBN-10: 0-13-368839-9, ISBN-13: 978-0-13-368839-9
79 Upper School
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