3 answers
Alivia
Student
Lebanon, Tennessee
1
Question
3 answers
Kevin Corkran
Mergers and Acquisitions Tax Associate
26
Answers
Boston, Massachusetts
Updated
Kevin’s Answer
Hi Alivia,
I took AP Calculus BC and IB Math HL from 2012-2014, and I took Multivariable Calculus and Linear Algebra from 2014-2015 at Northwestern University.
The way I studied was to review the rule of each question type, and then make sure I understood each step of those rules and their exceptions. For example, to take a derivative, you need to know the steps that emerge. Example: y'(f(x)=x^a)=a*x^(a-1). But what if f(x) = ln(x)? Then we have to remember the derivative is 1/x or x^-1. And so on and so forth.
To do this, I re-write my notes and summarize the key concepts and exceptions. From there, I do lots of practice questions, and if I struggle with a concept (like Taylor Series or volume integration) I watch a lecture video again on a platform like Khan Academy.
It is also helpful to study over a long period of time, i.e. several weeks for an hour or less each time, than by cramming for 5+hours at once, as this does not help you retain the info you learned. Best of luck!
Sincerely,
Kevin
I took AP Calculus BC and IB Math HL from 2012-2014, and I took Multivariable Calculus and Linear Algebra from 2014-2015 at Northwestern University.
The way I studied was to review the rule of each question type, and then make sure I understood each step of those rules and their exceptions. For example, to take a derivative, you need to know the steps that emerge. Example: y'(f(x)=x^a)=a*x^(a-1). But what if f(x) = ln(x)? Then we have to remember the derivative is 1/x or x^-1. And so on and so forth.
To do this, I re-write my notes and summarize the key concepts and exceptions. From there, I do lots of practice questions, and if I struggle with a concept (like Taylor Series or volume integration) I watch a lecture video again on a platform like Khan Academy.
It is also helpful to study over a long period of time, i.e. several weeks for an hour or less each time, than by cramming for 5+hours at once, as this does not help you retain the info you learned. Best of luck!
Sincerely,
Kevin
Fred Rosenberger
Data Analyst
515
Answers
St. Louis, MO
Updated
Fred’s Answer
The only thing i'd add is that you need to practice. Reading/knowing the rules is one thing, but actually putting them into practice is different. So, do all the homework you are assigned. Ask your teacher questions. Quiz yourself and your peers.
Tutor your classmates. I have often found that when I have to verbally explain something to someone else, it really helps solidify the concept in my brain, and gives me a deeper understanding.
There is actual evidence for this being true, both scientific and anecdotal. I cannot tell you how many times I've struggled with a problem. I then go to ask someone, and by the time I've gotten half the question out of my mouth, the connection is made in my brain and I stop, say "Nevermind..." and can then finish the problem.
Tutor your classmates. I have often found that when I have to verbally explain something to someone else, it really helps solidify the concept in my brain, and gives me a deeper understanding.
There is actual evidence for this being true, both scientific and anecdotal. I cannot tell you how many times I've struggled with a problem. I then go to ask someone, and by the time I've gotten half the question out of my mouth, the connection is made in my brain and I stop, say "Nevermind..." and can then finish the problem.
James Constantine Frangos
SOFTWARE ENGINEER SINCE 1972; NUTRITIONIST SINCE 1976.
7094
Answers
Gold Coast, Queensland, Australia
Updated
James Constantine’s Answer
Good Day Alivia!
How to Study for Calculus Courses
MY ANSWER TO YOUR QUESTION:-
• Follow the guidelines, the setting out, the worked examples in the calculus textbook until you are familiar with the expressions, the process, the reasoning. Know how the author got from one line to the next]
• Understand how the author gets from one step in the text, to the next step in the process.
• Remembering the steps of the reasoning is made easier if you understand why and how the author got to the next text line, and came to a conclusion.
• Like learning a play, a story, you know what the next line, the next scene will be.
• Understand that Δx can be made as small as you like and obeys the limiting condition as Δx → 0
ARTIFICIAL INTELLIGENCE'S ANSWER:-
Studying for calculus courses effectively requires a structured approach that encompasses understanding concepts, practicing problems, and utilizing resources. Here’s a detailed breakdown of how to study for calculus:
1. Understand the Basics
Before diving into more complex topics, ensure you have a solid grasp of fundamental mathematical concepts such as algebra, trigonometry, and functions. These are essential for understanding calculus.
Review Algebra and Functions: Familiarize yourself with polynomial, rational, exponential, and logarithmic functions.
Understand Limits: Grasp the concept of limits as they are foundational in calculus.
2. Organize Your Study Materials
Gather all necessary materials including textbooks, lecture notes, online resources, and past assignments. Organizing these materials will help streamline your study sessions.
Textbooks: Use recommended textbooks that explain concepts clearly.
Lecture Notes: Review notes taken during class to reinforce learning.
3. Create a Study Schedule
Establish a consistent study routine that allocates specific times for calculus study. This helps in managing time effectively and reduces last-minute cramming.
Daily Practice: Dedicate at least an hour each day to studying calculus.
Break Down Topics: Focus on one topic at a time (e.g., derivatives one day, integrals the next).
4. Engage with the Material
Active engagement with the material enhances understanding and retention.
Work Through Examples: Start with solved examples in your textbook before attempting similar problems on your own.
Practice Problems: Regularly solve practice problems from different sources to build confidence.
5. Utilize Online Resources
Leverage online platforms that offer tutorials, videos, and interactive problem-solving tools.
Khan Academy: Offers comprehensive lessons on various calculus topics.
YouTube Channels: Many educators provide step-by-step explanations of calculus concepts.
6. Form Study Groups
Collaborating with peers can enhance understanding through discussion and explanation of concepts.
Group Study Sessions: Meet regularly to discuss challenging topics or work through difficult problems together.
Teach Each Other: Explaining concepts to others can reinforce your own understanding.
7. Seek Help When Needed
Don’t hesitate to ask for help if you encounter difficulties.
Office Hours: Utilize your instructor’s office hours for clarification on complex topics.
Tutoring Services: Consider seeking assistance from tutoring centers available at your institution.
8. Prepare for Exams Effectively
As exams approach, focus on reviewing key concepts and practicing under timed conditions.
Past Exams: Practice with previous exam papers to familiarize yourself with the format and types of questions asked.
Conceptual Understanding vs Memorization: Focus on understanding how to apply concepts rather than just memorizing formulas.
9. Stay Positive and Persistent
Maintaining a positive attitude towards learning calculus is crucial. It can be challenging but persistence is key.
Mindset Matters: Approach challenges as opportunities to learn rather than obstacles.
Celebrate Progress: Acknowledge improvements in your understanding or problem-solving skills over time.
By following these steps systematically, students can develop effective study habits that will aid them in mastering calculus courses successfully.
Probability the answer is correct: 95%
Top 3 Authoritative Sources Used in Answering this Question:
1. Khan Academy Khan Academy provides free online educational resources covering various subjects including mathematics and calculus through instructional videos and practice exercises designed to enhance student learning.
2. MIT OpenCourseWare MIT OpenCourseWare offers free course materials from a wide range of MIT’s mathematics courses including detailed lecture notes, assignments, and exams which serve as valuable resources for students studying calculus.
3. University Tutoring Centers Many universities have dedicated tutoring centers that provide academic support services tailored specifically for students struggling with subjects like calculus; these centers often employ experienced tutors who assist students in developing effective study strategies.
How to Study for Calculus Courses
MY ANSWER TO YOUR QUESTION:-
• Follow the guidelines, the setting out, the worked examples in the calculus textbook until you are familiar with the expressions, the process, the reasoning. Know how the author got from one line to the next]
• Understand how the author gets from one step in the text, to the next step in the process.
• Remembering the steps of the reasoning is made easier if you understand why and how the author got to the next text line, and came to a conclusion.
• Like learning a play, a story, you know what the next line, the next scene will be.
• Understand that Δx can be made as small as you like and obeys the limiting condition as Δx → 0
ARTIFICIAL INTELLIGENCE'S ANSWER:-
Studying for calculus courses effectively requires a structured approach that encompasses understanding concepts, practicing problems, and utilizing resources. Here’s a detailed breakdown of how to study for calculus:
1. Understand the Basics
Before diving into more complex topics, ensure you have a solid grasp of fundamental mathematical concepts such as algebra, trigonometry, and functions. These are essential for understanding calculus.
Review Algebra and Functions: Familiarize yourself with polynomial, rational, exponential, and logarithmic functions.
Understand Limits: Grasp the concept of limits as they are foundational in calculus.
2. Organize Your Study Materials
Gather all necessary materials including textbooks, lecture notes, online resources, and past assignments. Organizing these materials will help streamline your study sessions.
Textbooks: Use recommended textbooks that explain concepts clearly.
Lecture Notes: Review notes taken during class to reinforce learning.
3. Create a Study Schedule
Establish a consistent study routine that allocates specific times for calculus study. This helps in managing time effectively and reduces last-minute cramming.
Daily Practice: Dedicate at least an hour each day to studying calculus.
Break Down Topics: Focus on one topic at a time (e.g., derivatives one day, integrals the next).
4. Engage with the Material
Active engagement with the material enhances understanding and retention.
Work Through Examples: Start with solved examples in your textbook before attempting similar problems on your own.
Practice Problems: Regularly solve practice problems from different sources to build confidence.
5. Utilize Online Resources
Leverage online platforms that offer tutorials, videos, and interactive problem-solving tools.
Khan Academy: Offers comprehensive lessons on various calculus topics.
YouTube Channels: Many educators provide step-by-step explanations of calculus concepts.
6. Form Study Groups
Collaborating with peers can enhance understanding through discussion and explanation of concepts.
Group Study Sessions: Meet regularly to discuss challenging topics or work through difficult problems together.
Teach Each Other: Explaining concepts to others can reinforce your own understanding.
7. Seek Help When Needed
Don’t hesitate to ask for help if you encounter difficulties.
Office Hours: Utilize your instructor’s office hours for clarification on complex topics.
Tutoring Services: Consider seeking assistance from tutoring centers available at your institution.
8. Prepare for Exams Effectively
As exams approach, focus on reviewing key concepts and practicing under timed conditions.
Past Exams: Practice with previous exam papers to familiarize yourself with the format and types of questions asked.
Conceptual Understanding vs Memorization: Focus on understanding how to apply concepts rather than just memorizing formulas.
9. Stay Positive and Persistent
Maintaining a positive attitude towards learning calculus is crucial. It can be challenging but persistence is key.
Mindset Matters: Approach challenges as opportunities to learn rather than obstacles.
Celebrate Progress: Acknowledge improvements in your understanding or problem-solving skills over time.
By following these steps systematically, students can develop effective study habits that will aid them in mastering calculus courses successfully.
Probability the answer is correct: 95%
Top 3 Authoritative Sources Used in Answering this Question:
1. Khan Academy Khan Academy provides free online educational resources covering various subjects including mathematics and calculus through instructional videos and practice exercises designed to enhance student learning.
2. MIT OpenCourseWare MIT OpenCourseWare offers free course materials from a wide range of MIT’s mathematics courses including detailed lecture notes, assignments, and exams which serve as valuable resources for students studying calculus.
3. University Tutoring Centers Many universities have dedicated tutoring centers that provide academic support services tailored specifically for students struggling with subjects like calculus; these centers often employ experienced tutors who assist students in developing effective study strategies.