"Developing tasks for non-homogeneous equations, the inspiration value has increased by 221 points. Even for a D-level difficulty, this is too high!"
"The task of partial differential equations also increased the inspiration value by nine points."
"Why is it so high?"
Wang Hao looked at the system display, carefully pondering. Because of last week's experience, he could be sure that more students paying attention in class was just one reason.
Three physics classes together only raised the inspiration value by four points, two points for the partial differential equation task.
So the reason was very direct—
Relevance!
"The increase in inspiration value is directly related to the content of the lectures!"
"Undergraduate-level non-homogeneous problems, just explaining one-dimensional non-homogeneous equations, are relatively simple. But non-homogeneous equations are a type of partial differential equation, researching methods for solving equations, in a broader sense, can also be considered 'common methods for solving specific partial differential equations.'"
"Task two is where the difficulty lies."
"The research related to one-dimensional non-homogeneous equations only has a D-level difficulty, lower even than Fourier transforms. Obtaining a large amount of inspiration value can also be understood!"
Of course, there is also the possibility that some students diverged in thought during class, finding one or several correct research directions.
Research, inspiration is crucial.
No amount of effort can compare to a sudden inspiration, which is quite normal in research. Students might not know if their divergent thinking or ideas are correct research directions, but the system can determine and provide feedback.
This is impossible to judge.
Wang Hao went to the cafeteria for lunch. After filling his stomach, he immediately returned to the office.
Several people were in the office.
Yan Jing asked, "Wang Hao, how was the class?" She was asking about the reported incident, and everyone in the office knew about it.
Wang Hao replied, "Two administrative staff came, but it seems like they didn't do anything and left after class."
"That's good."
Zhu Ping added, "Don't worry. Administration generally won't target lecturers. Being a bit strict with students is fine. But nowadays, students are hard to manage. If something happens, some of them just post it online."
"I sometimes worry during lectures."
Zhang Zhiqiang chimed in, "I'm afraid of messing up during class. If something goes wrong and it gets posted online... it would be embarrassing..."
The office discussion revolved around this issue.
Wang Hao also added, "I directly deduct participation points if I catch anyone using their phones during class. They don't dare to mess with me!"
"You're tough!"
"It's not something one can learn." Yan Jing shook her head. "Students are just too difficult to manage. Honestly, I sometimes still feel like a student myself!"
Zhu Ping laughed, "You do look younger, a bit cute."
"Haha."
Several people joined in the laughter.
Yan Jing felt a bit embarrassed, glanced at Wang Hao, and found him focused on something again.
They say that serious men are the most charming...
She stared at Wang Hao for a moment, her face suddenly turning red. She looked around pretending not to care, quickly shifting her gaze elsewhere.
Wang Hao chatted with the others in the office for a while, then noticed that Zheng Yaojun had sent something— it was the content for the "Differential Equations" class, including some basics from the textbook, several problems to be discussed in class, and a few homework exercises.
The first-year graduate course "Differential Equations" is a crucial course for science majors like mathematics and physics.
At the undergraduate level, there's "Partial Differential Equations," with most of the content being basic knowledge, such as "non-homogeneous," "Fourier transform," "higher-dimensional problems," and so on. Slightly more complex content only requires a basic understanding.
At the graduate level, "Differential Equations" builds on this foundation.
Courses like "Mathematical Analysis," "Advanced Algebra," "Analytical Geometry," and "Ordinary Differential Equations" are prerequisites for the graduate-level "Differential Equations" course.
Because it was the latter part of the semester, the course had reached its most complex stage. The content provided for the next two classes, covering four hours in total, mainly focused on two topics—
One was the graphical solutions of systems of differential equations;
The other was solving non-homogeneous linear equations.
Wang Hao couldn't help but smile when he saw the latter topic. He was currently teaching "One-Dimensional Non-Homogeneous Equations." Teaching another class on "Solving Non-Homogeneous Linear Equations" for the first-years would certainly bring in a lot of inspiration points.
One thirty.
The office became much quieter as several teachers went to their classes.
Wang Hao officially entered work mode. Spending a "teaching coin" to enter concentration mode, he then opened the task module.
[Task 2]
[Research Project Name: In-depth Study of One-Dimensional Non-Homogeneous Equation Solutions (Difficulty: D).]
[Inspiration Value: 243.]
(Tip: You can use 100 inspiration points to assist in obtaining interrelated inspiration and knowledge for research.)
"Use!"
[Task 2, Inspiration Value -100.]
Suddenly, related inspirations about non-homogeneous equations formed a complete and clear structure in his mind.
A pathway had been opened.
"I can summarize and generalize high-order differential equations, categorizing them into several types that can be transformed into homogeneous equations for solution..."
"That's right!"
The consumption of inspiration points wasn't just about acquiring new knowledge out of thin air; it was about organizing and clarifying existing knowledge and ideas in one's mind.
It was like activating inspiration!
Wang Hao immediately knew what to do. He conducted specific research, listing out several types of high-order differential equations that could be transformed into homogeneous equations and then transformed them one by one using specific methods.
Through continuous transformations and calculations, he identified their common characteristics and summarized them.
The research was quickly completed.
Because he already had relevant knowledge in his mind and the inspiration had directed him towards a direction, it was almost like simply putting it down on paper.
"This research... is indeed at a D-level!"
Looking at the summarized content on paper, Wang Hao couldn't help but shake his head. In comparison, the research level and the studies he remembered from his Ph.D. days were similar.
A paper could definitely be written.
Because it was just summarizing several methods of solving equations, the outcome could only be considered very minor, enough for just a small paper.
Then, he spent another hundred inspiration points.
This time, the inspiration was related to the complex non-homogeneous p-Kirchhoff elliptic equation system. It involved researching a class of non-homogeneous p-Kirchhoff elliptic equation systems and confirming the existence of multiple solutions.
Again, it was a very minor research.
"It seems that D-level is just at this level."
Wang Hao felt a bit helpless, but upon careful consideration, he couldn't be completely certain. "D-level, low difficulty, usually results in small achievements. But it's also possible that there are some applications or problems that others haven't thought of, which could lead to significant achievements."
Difficulty doesn't necessarily correlate with the size of achievements.
It could only be said that low-difficulty research generally results in smaller achievements, but there's still a possibility of significant outcomes.
Of course, being able to come up with two research directions and corresponding results in just one class session was quite remarkable.
Although the results were somewhat trivial, they could still add to someone else's research record.
...
Wang Hao left quite early.
After having dinner at the cafeteria around five o'clock, he took a stroll, then went straight home.
He listened to music while working on his paper.
There was a knock on the door.
Wang Hao opened it with a puzzled expression and found the two girls from across the hall. He asked, "What's up?"
Li Qian just looked at him.
Gu Youyou held a book and stared earnestly into his eyes, saying, "Can you help us with a problem?"
"What problem?"
"Differential equations."
"Sure, come in!" Wang Hao made room for them to sit on the sofa and then brought two bottles of drinks as refreshments.
Gu Youyou handed him a piece of paper with the problem written on it.
She stared at Wang Hao's eyes the whole time.
Wang Hao felt awkward being stared at like that. If he had any narcissistic tendencies, he would have thought she was interested in him...
Wait!
It's not interest, it's suspicion!
"It's like being stared at by the police, like I've become a suspect," Wang Hao thought strangely, assuming it was just her personality.
He glanced at the paper, "Solving Differential Equation Systems with Linear Algebra."
"This problem... is simple!"
Wang Hao knew how to solve it with just a glance. He wrote down the answer and explained, "First, we need to represent the equations with matrices, like this..."
"Then we express the general solution with matrices. Let's assume the form of the solutions as..."
"Then we substitute and simplify the equations, finding the eigenvalues."
"Look at this equation. Substitute λ1 and λ2 into the equation and find the eigenvectors..."
Wang Hao explained continuously, taking about five minutes in total.
The time spent actually solving the problem was less than two minutes combined, as if he were writing down the answers directly, with the rest of the time spent on explanation.
Gu Youyou and Li Qian nodded along. They seemed to be thinking along with him but didn't show as much surprise as last time.
They exchanged a glance, showing a mysterious expression on their faces.
When Wang Hao finished explaining, Gu Youyou and Li Qian stood up to leave. Suddenly, Wang Hao said, "Don't leave yet. I have something to ask you."
They sat back down.
Wang Hao observed their expressions and behavior, feeling something was off, but women's minds were too complicated, so he didn't dwell on it and asked, "You've just learned about solving differential equation systems with linear algebra, right?"
"Yes."
Wang Hao began to ask seriously, "How did you feel about it? Did you find it difficult? Your homework didn't seem hard; did you struggle while.